双层非线性隔振系统的动力学分析及时延混沌化
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摘要
隔振是抑制潜艇动力机械振动向艇体传递最常用的手段。利用非线性隔振系统处于混沌状态时其响应功率谱呈连续谱这一特点，可以降低和改变动力机械传递到艇体的线谱特征，从而降弱潜艇辐射水声的线谱成分，提高潜艇的水声隐身性能，即线谱混沌化控制方法。为此，论文主要完成了两个方面的研究工作：深入研究了两自由度非线性隔振系统动力学特性；针对实际应用线谱混沌化控制方法时面临的如何保持非线性隔振系统的混沌状态和实现小振幅下的混沌这两个难点，提出了相应的混沌反控制方法。其研究工作不仅丰富了非线性动力学和混沌控制理论，同时，具有重要的工程应用价值。围绕上述问题所开展的具体研究内容包括：
将三维实体隔振模型简化为梁模型，采用欧拉-伯努利梁假设，考虑几何非线性，分析了由非线性隔振器连接的两层耦合梁的静动力学行为。采用微分求积法或伽辽金法将偏微分平衡方程转化为仅与时间有关的微分方程，再通过Newmark或龙哥库塔数值积分求解。将求得的耦合梁静变形结果与ANSYS结果进行比较，并分析了耦合梁的动力学行为。
将隔振系统简化为两自由度质量弹簧系统，即在被隔振机器与基础之间设置非线性隔振浮筏，引入位移反馈控制技术。采用平均法得到了非线性隔振系统的渐近解，研究了其非线性动力学行为。通过数值算例，讨论了系统各参数对动力学行为的影响，利用分岔图研究了系统的运动状态随外激励频率以及控制增益改变时的系统响应变化。
采用广义混沌同步化原理的控制方法，将Lorenz系统族，如Lorenz系统、Chen系统、Lü系统、R ssler系统以及Chua系统作为驱动信号，通过调节驱动系统控制参数使之产生混沌响应，通过混沌同步化原理来混沌化非线性隔振系统，从而将潜艇工作时辐射出的特征线谱转化为混沌谱。并且，采用隐式性能指标函数及Hooke-Jeeves优化方法，来求得最优控制增益，从而得到具有较好品质的混沌谱特征。通过数值算例，分析了双层隔振系统的动力学行为，并比较了Lorenz系统族各系统的混沌化效果。
引入时延控制方法使得隔振系统高维度化，有利于混沌化的实现。将非线性隔振系统在平衡点处线性化，并通过Laplace变换得到系统的特征方程。由于时延的引入，系统特征方程为超越方程，具有无数个特征根，即时延系统的无穷维性质。时延系统的特征根与时延相关，采用了广义Strum准则来预测特征根的分布，从而分析时延浮筏系统的稳定性，得到了时延无关稳定区间的临界控制增益，并得到了稳定性转换时的临界时延，分析了其稳定与不稳定区间。应用数值算例验证了理论结果的正确性，并且分析了系统参数的变化对临界控制增益的变化。
考虑在小阻尼、小控制增益以及小幅值激励情况下，采用多尺度法分析时延控制非线性隔振系统主共振以及1:1內共振时的渐近解，得到含有时延的平均方程，通过分析其平衡解及其稳定性来研究时延反馈控制参数以及系统参数对系统动力学行为的影响。数值结果证明，通过调节不同的控制参数，可以控制系统的振动幅值，分析振动幅值随着时延的变化规律，因此可以通过调节系统参数以及控制时延来减振。系统解的稳定性随着时延变化而变化，通过与分岔图比较，发现不稳定区域对应着动力系统的混沌区域。
分析了具有双重时延隔振系统的稳定性。对于具有两相等时延的动力学系统，采用广义Strum准则可以得到时延无关稳定性的临界控制增益，以及稳定性切换时的临界时延条件。对于具有不同时延的动力系统，采用了二次特征值法，避免了繁琐的系数推导，采用矩阵及算子运算可求得时延特征方程的特征根以及临界时延，从而研究双时延控制隔振系统的稳定性。得到了时延无关稳定性的临界控制增益区域，并求得了系统稳定与不稳定边界的临界时延。分析了不同控制参数，控制形式对系统混沌化以及降低线谱的效果，并比较了单时延系统与双时延系统的稳定区域以及混沌化效果。
Vibration isolation is the most frequently used approach to isolate the machineryvibration from transmitting to the submarine. According to the broad spectra feature ofchaos, chaotification of the nonlinear vibration isolation system is employed to reducethe line spectra of the submarine, in order to enchance its stealth capability. In thisdissertation，two aspects of research are conducted. The nonlinear dynamic behaviorof the2degree of freedom (dof) nonlinear vibration isolation system is studed. Basedon the idea of reducing the line spectrum by chaotification, one challenge is how toprovoke chaos and maintain chaos. Another hinder is that how to induce chaos withtiny energy. In order to cope with these difficulties, several control methods areempoyed in the dissertation. The research results are significant not only in theacademic but also in the practical engineering. The main results contain as follows.
By simplifing the three dimensional vibration isolation model into onedimentional beam, adopting the Euler-Bounuli hipotheis, and considering thegeometric nonlinearity, the static and dynamic behavior of the two layer beamscoupled by nonlinear isolators are investigated. The Differential-Quadrature methodand Galerkin method are employed to convert the partial differential motion equationsinto differential equation with respect to time. By Nermark or Longe-Kutta method,the differential equaiton can be integrated numerically. The static deformation of thebeams are compared with the results obtained by comercial software ANSYS.
The two-layer vibration isolation system is further simplifed into a2-dofmass-spring system. The passive vibration isolation approach is adopted byintroducing floating raft and nonlinear isolators. The linear feedback control is alsoimplemented to the vibration isolation system. The approximate solution of thenonlinear vibration isolation system is obtained by average method and the nonlineardynamic behavior is studied. According to numerical simulation, the effect of systemparameters on the dynamic behavior of the system is discussed. The bifucationdiagrams show the viaraiotn of the system motion states with respect to the excitingfrequency and control gain.
The generalized chaotic synchorization method is employed by using theresponse of the Lorenz system family, such as Lorenz system, Chen system, Lü system,R ssler system and Chua system, as driving signal. When the drive system is set tohaving chaotic attrators, the chaotic signal is used to synchorize the vibration isolationsystem to be chaotic. The Hooke-Jeeves optimazation method and implicit index function are used to optimize the control gain in order to obtain chaos with betterquality. By numerical simulation, the dynamic behavior of the vibraiton isolationsystem is studied and the chaotification effect of the Lorenz system family isinvestigated.
The time delay can make the vibration isolation system have infinite dimension,which makes the ease of chaotification. The nonlinear vibration isolation system islinearized at the equilibrium point and the characteristic equation is obtained byLaplace transformation. Due to the time delay, the characteristic eqation is atranscendental equation, which has infinite eigenvalues, that is, the infinite dimensionof the time delay system. As for the time delay system, the stability of the sytem isassociated with time delay. The general strum criterion is adopted to predicte thedistribution of the roots. Then the critical control gain for the delay-independentstaiblity is obtained and the critical time delays for the stability change are studied.The numerical cases are investigated to verify the correctness of the theoreticalconclusion.
Assuming the vibration isolation has small damping, small control gain and smallexciting amplitude, the multiscale method is used to obtain the approximate solutionof the nonlinear vibration isolation system under primary and1:1resonance. Theaverage equation involving time delay is obtained. By investigating the equilibriumsolution and the stabilty, the effect of system paramters and time delay controlparameters on the dynamic behavior of the system is studied. The results show that byadjusting the control parameters the vibraiton amplitude of the system can becontrolled. The vibration amplitude is changed with increase of time delay. Thereforethe system paramters can be tuned to reduce the vibration amplitude. The stability ofthe system also depends on the time delay control setting. With comparison withbifurcation diagram, the unstable region corresponds to chaotic region correctly.
Stability of the sytem with dual time delay control is studied. When the dual timedelay control has the same delay, the generalized strum method can be used. Whenthey are unequal, the quadratic eigenvalue method is adopted. By matrix and operatorcomputation the eigenvalue of the characteristic equaiton and critical time delay areobtained. The delay-independent stability region is obtained and the critical time delayof stability change is attained. Effects of different control parameter, control scheme on chaotification of the vibraiton isolation system are investigated. The stabilityregion and chaotification effect of single time delay and dual time delay are compared.
将三维实体隔振模型简化为梁模型，采用欧拉-伯努利梁假设，考虑几何非线性，分析了由非线性隔振器连接的两层耦合梁的静动力学行为。采用微分求积法或伽辽金法将偏微分平衡方程转化为仅与时间有关的微分方程，再通过Newmark或龙哥库塔数值积分求解。将求得的耦合梁静变形结果与ANSYS结果进行比较，并分析了耦合梁的动力学行为。
将隔振系统简化为两自由度质量弹簧系统，即在被隔振机器与基础之间设置非线性隔振浮筏，引入位移反馈控制技术。采用平均法得到了非线性隔振系统的渐近解，研究了其非线性动力学行为。通过数值算例，讨论了系统各参数对动力学行为的影响，利用分岔图研究了系统的运动状态随外激励频率以及控制增益改变时的系统响应变化。
采用广义混沌同步化原理的控制方法，将Lorenz系统族，如Lorenz系统、Chen系统、Lü系统、R ssler系统以及Chua系统作为驱动信号，通过调节驱动系统控制参数使之产生混沌响应，通过混沌同步化原理来混沌化非线性隔振系统，从而将潜艇工作时辐射出的特征线谱转化为混沌谱。并且，采用隐式性能指标函数及Hooke-Jeeves优化方法，来求得最优控制增益，从而得到具有较好品质的混沌谱特征。通过数值算例，分析了双层隔振系统的动力学行为，并比较了Lorenz系统族各系统的混沌化效果。
引入时延控制方法使得隔振系统高维度化，有利于混沌化的实现。将非线性隔振系统在平衡点处线性化，并通过Laplace变换得到系统的特征方程。由于时延的引入，系统特征方程为超越方程，具有无数个特征根，即时延系统的无穷维性质。时延系统的特征根与时延相关，采用了广义Strum准则来预测特征根的分布，从而分析时延浮筏系统的稳定性，得到了时延无关稳定区间的临界控制增益，并得到了稳定性转换时的临界时延，分析了其稳定与不稳定区间。应用数值算例验证了理论结果的正确性，并且分析了系统参数的变化对临界控制增益的变化。
考虑在小阻尼、小控制增益以及小幅值激励情况下，采用多尺度法分析时延控制非线性隔振系统主共振以及1:1內共振时的渐近解，得到含有时延的平均方程，通过分析其平衡解及其稳定性来研究时延反馈控制参数以及系统参数对系统动力学行为的影响。数值结果证明，通过调节不同的控制参数，可以控制系统的振动幅值，分析振动幅值随着时延的变化规律，因此可以通过调节系统参数以及控制时延来减振。系统解的稳定性随着时延变化而变化，通过与分岔图比较，发现不稳定区域对应着动力系统的混沌区域。
分析了具有双重时延隔振系统的稳定性。对于具有两相等时延的动力学系统，采用广义Strum准则可以得到时延无关稳定性的临界控制增益，以及稳定性切换时的临界时延条件。对于具有不同时延的动力系统，采用了二次特征值法，避免了繁琐的系数推导，采用矩阵及算子运算可求得时延特征方程的特征根以及临界时延，从而研究双时延控制隔振系统的稳定性。得到了时延无关稳定性的临界控制增益区域，并求得了系统稳定与不稳定边界的临界时延。分析了不同控制参数，控制形式对系统混沌化以及降低线谱的效果，并比较了单时延系统与双时延系统的稳定区域以及混沌化效果。
Vibration isolation is the most frequently used approach to isolate the machineryvibration from transmitting to the submarine. According to the broad spectra feature ofchaos, chaotification of the nonlinear vibration isolation system is employed to reducethe line spectra of the submarine, in order to enchance its stealth capability. In thisdissertation，two aspects of research are conducted. The nonlinear dynamic behaviorof the2degree of freedom (dof) nonlinear vibration isolation system is studed. Basedon the idea of reducing the line spectrum by chaotification, one challenge is how toprovoke chaos and maintain chaos. Another hinder is that how to induce chaos withtiny energy. In order to cope with these difficulties, several control methods areempoyed in the dissertation. The research results are significant not only in theacademic but also in the practical engineering. The main results contain as follows.
By simplifing the three dimensional vibration isolation model into onedimentional beam, adopting the Euler-Bounuli hipotheis, and considering thegeometric nonlinearity, the static and dynamic behavior of the two layer beamscoupled by nonlinear isolators are investigated. The Differential-Quadrature methodand Galerkin method are employed to convert the partial differential motion equationsinto differential equation with respect to time. By Nermark or Longe-Kutta method,the differential equaiton can be integrated numerically. The static deformation of thebeams are compared with the results obtained by comercial software ANSYS.
The two-layer vibration isolation system is further simplifed into a2-dofmass-spring system. The passive vibration isolation approach is adopted byintroducing floating raft and nonlinear isolators. The linear feedback control is alsoimplemented to the vibration isolation system. The approximate solution of thenonlinear vibration isolation system is obtained by average method and the nonlineardynamic behavior is studied. According to numerical simulation, the effect of systemparameters on the dynamic behavior of the system is discussed. The bifucationdiagrams show the viaraiotn of the system motion states with respect to the excitingfrequency and control gain.
The generalized chaotic synchorization method is employed by using theresponse of the Lorenz system family, such as Lorenz system, Chen system, Lü system,R ssler system and Chua system, as driving signal. When the drive system is set tohaving chaotic attrators, the chaotic signal is used to synchorize the vibration isolationsystem to be chaotic. The Hooke-Jeeves optimazation method and implicit index function are used to optimize the control gain in order to obtain chaos with betterquality. By numerical simulation, the dynamic behavior of the vibraiton isolationsystem is studied and the chaotification effect of the Lorenz system family isinvestigated.
The time delay can make the vibration isolation system have infinite dimension,which makes the ease of chaotification. The nonlinear vibration isolation system islinearized at the equilibrium point and the characteristic equation is obtained byLaplace transformation. Due to the time delay, the characteristic eqation is atranscendental equation, which has infinite eigenvalues, that is, the infinite dimensionof the time delay system. As for the time delay system, the stability of the sytem isassociated with time delay. The general strum criterion is adopted to predicte thedistribution of the roots. Then the critical control gain for the delay-independentstaiblity is obtained and the critical time delays for the stability change are studied.The numerical cases are investigated to verify the correctness of the theoreticalconclusion.
Assuming the vibration isolation has small damping, small control gain and smallexciting amplitude, the multiscale method is used to obtain the approximate solutionof the nonlinear vibration isolation system under primary and1:1resonance. Theaverage equation involving time delay is obtained. By investigating the equilibriumsolution and the stabilty, the effect of system paramters and time delay controlparameters on the dynamic behavior of the system is studied. The results show that byadjusting the control parameters the vibraiton amplitude of the system can becontrolled. The vibration amplitude is changed with increase of time delay. Thereforethe system paramters can be tuned to reduce the vibration amplitude. The stability ofthe system also depends on the time delay control setting. With comparison withbifurcation diagram, the unstable region corresponds to chaotic region correctly.
Stability of the sytem with dual time delay control is studied. When the dual timedelay control has the same delay, the generalized strum method can be used. Whenthey are unequal, the quadratic eigenvalue method is adopted. By matrix and operatorcomputation the eigenvalue of the characteristic equaiton and critical time delay areobtained. The delay-independent stability region is obtained and the critical time delayof stability change is attained. Effects of different control parameter, control scheme on chaotification of the vibraiton isolation system are investigated. The stabilityregion and chaotification effect of single time delay and dual time delay are compared.
引文
[1]朱石坚,何琳.船舶机械振动控制[M].北京:国防工业出版社,2006.
[2]朱英富,张国良.舰船隐身技术[M].哈尔滨:哈尔滨工程大学出版社,2003.
[3]孟晓宇,肖国林,陈虹.国外潜艇声隐身技术现状与发展综述[J].舰船科学技术,33(11):135-139.
[4]郑兆宁,向大威.水声信号被动检测与参数估计理论[M].北京:科学出版社,1983.
[5] Snowdon JC. Vibration isolation: use and characterization[J]. The Journal of theAcoustical Society of America,1979,66(5):1245-1274.
[6] Howard CQ. Recent Developments in Submarine Vibration Isolation and NoiseControl: proceedings of the Conference2011Presentations&Proceedings onUSB,2011[C].
[7]马运义,黄白,伏同先.船舶振动控制[M].大连,1992.
[8]丁文镜.减振理论[M].北京:清华大学出版社,1988.
[9]朱石坚,楼京俊,何其伟.振动理论与隔振技术[M].北京:国防工业出版社,2006.
[10] Nayfeh TA, Emaci E, Vakakis AF. Application of nonlinear localization to theoptimization of a vibration isolation system[J]. AIAA journal,1997,35(8):1378-1386.
[11] Ibrahim RA. Recent advances in nonlinear passive vibration isolators[J]. Journalof sound and vibration,2008,314(3-5):371-452.
[12] Fidlin A. Nonlinear oscillations in mechanical engineering[M]. Springer Verlag,2006.
[13] Zhang JZ, Li DD, Shen D. Study on Euler spring used in ultra–low frequencyvertical vibration isolation system[J]. Journal of Mechanical Strength,2004,3(26):237–241.
[14] Vakakis AF, Manevitch LI, Gendelman O et al. Dynamics of linear discretesystems connected to local, essentially non-linear attachments[J]. Journal ofsound and vibration,2003,264(3):559-577.
[15] Zhang JZ, Li D, Chen MJ et al. An ultra-low frequency parallel connectionnonlinear isolator for precision instruments[J]. Key Engineering Materials,2004,257:231-238.
[16] Casati G, Ford J, Casati G et al. Stochastic behavior in classical and quantumhamiltonian systems[M]. Springer-Verlag,1979.
[17] Li TY, Yorke JA. Period three implies chaos[J]. The American MathematicalMonthly,1975,82(10):985-992.
[18]陈式刚.映象与混沌[M].北京:国防工业出版社,1992.
[19]郝柏林.从抛物线谈起-混沌动力学引论[M].上海:上海科技教育出版社,1993.
[20]钱伟长.非线性力学的新发展-稳定性、分叉、突变、浑沌[M].武汉:华中理工大学出版社,1988.
[21]胡岗.随机力与非线性系统[M].上海:上海科技教育出版社,1994.
[22]郝柏林.分岔、混沌、奇怪吸引子、湍流及其他[J].物理学进展,1983,3(3):329-416.
[23]龙运佳,王聪玲,张平.基于混沌理论的振动压路机[J].中国农业大学学报,1998,3(002):19-22.
[24]龙运佳,杨勇.重型自行式混沌振动压路机[J].中国农业大学学报,2000,5(002):12-14.
[25] Lou JJ, Zhu SJ, He L et al. Application of chaos method to line spectrareduction[J]. Journal of sound and vibration,2005,286(3):645-652.
[26]朱石坚.线谱激励的混沌隔振研究[J].海军工程大学学报,2003,15.
[27] Jiang RJ, Zhu SJ. Vibration isolation and chaotic vibration: proceedings of theProceedings of the ASME International Design Engineering TechnicalConferences and Computers and Information in Engineering Conference－DETC2005, Chicago,2005[C]. ASME.
[28] Zhu SJ, Zheng YF, Fu YM. Analysis of non-linear dynamics of atwo-degree-of-freedom vibration system with non-linear damping and non-linearspring[J]. Journal of sound and vibration,2004,271(1-2):15-24.
[29]楼京俊,朱石坚.混沌隔振方法研究[J].船舶力学,2007,10(5):135-141.
[30] Jing-jun L, Qi-wei H, Shi-jian Z. Chaos in the softening duffing system undermulti-frequency periodic forces[J]. Applied Mathematics and Mechanics,2004,25(12):1421-1427.
[31] He QW, Zhu SJ, Lou JJ. Study on the computation method of piecewise linearsystem[J]. Dynamics of Continuous，Discrete，Impulsive Systems–Series A–Mathematical Analysis,2006,13:1400–1404.
[32] Yu X, Zhu S, Liu S. A new method for line spectra reduction similar togeneralized synchronization of chaos[J]. Journal of sound and vibration,2007,306(3-5):835-848.
[33]何琳,姚耀中.潜艇声隐身技术研究进展[J].舰船科学技术,2007,29(5):29-43.
[34]王国治.浮筏隔振装置抗基础冲击的研究[J].噪声与振动控制,2000,(6):10-13.
[35]赵应龙,何琳,吕志强.应用DDAM进行船舶浮筏隔振装置抗冲击计算[J].工程力学,2007,24(4):159-167.
[36]束立红,胡宗成,吕志强.国外舰船隔振器研究进展[J].舰船科学技术,2006,28(003):109-112.
[37]戴德沛.阻尼技术的工程应用[M].清华大学出版社,1991.
[38]张平宽.薄膜阻尼技术在电冰箱压缩机噪声控制中的应用[J].哈尔滨理工大学学报,1998,3(002):40-42.
[39]何琳.潜艇声隐身技术进展[J].舰船科学技术,2007,29(5):9-17.
[40]郭日修,朱云翔.船舶防振减振技术的进展[J].振动与冲击,1993,12(003):36-48.
[41]吴广明,沈荣瀛,李俊等.多层隔振系统的动力学模型[J].振动与冲击,2005,24(002):16-20.
[42]贺华,冯奇.双层隔振系统动力学建模和响应计算[J].同济大学学报:自然科学版,2004,32(012):1578-1582.
[43]王志刚,冯奇,汪玉.弹性浮筏系统动力学建模及冲击响应分析[J].船舶力学,2005,9(006):113-125.
[44]束立红,胡宗成,吕志强.国外舰船隔振器研究进展[J].舰船科学技术,2006,28(23).
[45] Kim S, Singh R. Vibration transmission through an isolator modelled bycontinuous system theory[J]. Journal of sound and vibration,2001,248(5):925-953.
[46]吕志强,黄映云,赵应龙等.浮筏隔振装置设计中的模态控制研究[J].振动工程学报,2004,17.
[47]陈安华,高威,高永毅.被动隔振的非线性动力学研究[J].中国机械工程,2008,19(9).
[48] Yu X, Zhu SJ, Liu SY. Bifurcation and chaos in multi-degree-of-freedomnonlinear vibration isolation system[J]. Chaos, Solitons&Fractals,2008,38(5):1498-1504.
[49]俞翔,姜荣俊,朱石坚.非线性隔振系统周期解的全局性态分析: proceedingsof the2002年全国振动工程及应用学术会议论文,北京,2002[C].
[50] Yu X., Zhu S., Lou J. Bifurcation analysis of nonlinear vibration isolation withhard stiffness by cell mapping[J]. Proceedings of the ASME Design EngineeringTechnical Conference on Mechanical Vibration and Noise, Chicago, IL, USA,2003,5B:1615–1619.
[51] Zhou Y. F., Tang J. Y., H. HX. Response and transmissibility of strong nonlinearactive isolation system[J]. Journal of Central South University (Science andTechnology),2005,36:496–500.
[52]姜荣俊.混沌隔振装置的设计[J].海军工程大学学报,2003,15.
[53]张磊,付永领,刘永光等.主动隔振技术及其应用与发展[J].机床与液压,2005,(002):5-8.
[54]杨铁军,靳国永,李玩幽等.舰船动力装置振动主动控制技术研究[J].舰船科学技术,2006,(0z2):46-53.
[55]顾仲权,马扣根,陈卫东等.振动主动控制[M].国防工业出版社,1997.
[56]贾玉红,王建军.飞机起落架的主动控制与半主动控制研究[J].兵工学报,2006,27(003):528-532.
[57]胡海岩,郭大蕾.振动半主动控制技术的进展[J].振动测试与诊断,2001,21(4):235-244.
[58]王加春,李旦.机械振动主动控制技术的研究现状和发展综述[J].机械强度,2001,23(2):156-160.
[59]徐洋,华宏星,张志谊等.舰船主动隔振技术综述[J].舰船科学技术,2009,30(2):27-33.
[60]周临震,刘德仿.电动式激振器骨架的形状优化设计[J].机械工程师,2006,(003):61-63.
[61]张洪田,李玩幽.电动式主动吸振技术研究[J].振动工程学报,2001,14(001):113-117.
[62]张磊,束立红,刘永光等.基于CMAC网络的主动隔振控制技术[J].机械科学与技术,2006,25(10):1160-1162.
[63]张磊,刘永光,付永领等.基于磁致伸缩作动器的主动隔振系统分析[J].航空动力学报,2005,19(6):782-785.
[64]夏兆旺,杨绍普,金宝宁等.基于磁流变液的半主动控制研究[J].现代机械,2005,(006):25-26.
[65]王炅,黄文良.磁流变减振器在半主动振动控制中的应用[J].南京理工大学学报:自然科学版,2004,28(3):269-272.
[66] Howard CQ. Technologies for the Management of the Acoustic Signature of aSubmarine: proceedings of the Proceedings of the Submarine Institute ofAustralia2010: SIA5th Biennial Conference,2010[C].
[67] Drathen AV. Propulsion system solutions for present and future naval vessels:proceedings of the Pacific, Sydney, Australia,27-29January,2010[C].
[68]束立红,范名琦.基于磁致伸缩作动器的主动隔振实验研究[J].振动与冲击,2006,25(5).
[69]陈士华,陆君安.混沌动力学初步[M].武汉水利电力大学出版社,1998.
[70]刘增荣.混沌的微扰判据[M].上海:上海科技教育出版社.1994.
[71] Ott E. Chaos in dynamical systems[M]. Cambridge Univ Pr,2002.
[72] Lorenz EN. Deterministic nonperiodic flow[J]. Journal of the atmosphericsciences,1963,20(2):130-141.
[73]龙运佳.混沌振动研究[J].方法与实践北京:清华大学出版社,1997,4.
[74]吴祥兴,陈忠.混沌学导论[M].上海科学技术文献出版社,1996.
[75]张琪昌,王洪礼,竺致文.分岔与混沌理论及应用[M].天津大学出版社,2005.
[76]舒仲周,张继业,曹登庆.运动稳定性[M].中国铁道出版社,2001.
[77]王洪礼,张琪昌,郭树起.非线性动力学理论及其应用[M].天津科学技术出版社,2002.
[78] Bondaryk JE. Vibration of truss structures[J]. The Journal of the AcousticalSociety of America,1997,102:2167.
[79] Steliana C. Desynchronization and chaotification of nonlinear dynamicalsystems[J]. Chaos, Solitons and Fractals,2005,24:1307–1315.
[80] Chen HK, Lin TN, Chen JH. Dynamic analysis, controlling chaos andchaotification of a SMIB power system[J]. Chaos, Solitons and Fractals,2005,24:1307–1315.
[81] Mohamed Z, Ahmed O, Nejib S. Controlling chaos in the permanent magnetsynchronous motor[J]. Chaos, Solitons and Fractals,2009,41:1266–1276.
[82] Chen HK, Ge ZM. Bifurcations and chaos of a two-degree-of-freedomdissipative gyroscope[J]. Chaos, Solitons&Fractals,2005,24(1):125-136.
[83] Ge ZM, Cheng JW, Chen YS. Chaos anticontrol and synchronization of threetime scales brushless DC motor system[J]. Chaos, Solitons&Fractals,2004,22(5):1165-1182.
[84] Moukam Kakmeni FM, Bowong S, Tchawoua C et al. Chaos control andsynchronization of a Φ6-Van der Pol oscillator[J]. Physics Letters A,2004,322(5):305-323.
[85] Carrella A, Brennan MJ, Waters TP et al. On the design of ahigh-static-low-dynamic stiffness isolator using linear mechanical springs andmagnets[J]. Journal of sound and vibration,2008,315(3):712-720.
[86] Eissa M, Bauomy HS, Amer YA. Active control of an aircraft tail subject toharmonic excitation[J]. Acta Mechanica Sinica,2007,23(4):451-462.
[87] Sheu LJ, Chen HK, Chen JH et al. Chaotic dynamics of the fractionally dampedDuffing equation[J]. Chaos, Solitons&Fractals,2007,32(4):1459-1468.
[88] Lee CM, Goverdovskiy VN, Temnikov AI. Design of springs with "negative"stiffness to improve vehicle driver vibration isolation[J]. Journal of sound andvibration,2007,302(4):865-874.
[89] Jing XJ, Lang ZQ. Frequency domain analysis of a dimensionless cubicnonlinear damping system subject to harmonic input[J]. Nonlinear Dynamics,2009,58(3):469-485.
[90] Yassen MT. Chaos control of chaotic dynamical systems using backsteppingdesign[J]. Chaos, Solitons&Fractals,2006,27(2):537-548.
[91]胡岗,萧井华,郑志刚.混沌控制[M].上海:上海科技教育出版社,2000.
[92]王光瑞,陈式刚.混沌的控制、同步与应用[M].北京:国防工业出版社,2001.
[93] Chen G, Dong X. From chaos to order: methodologies, perspectives andapplications[M]. Singapore: World Scientific,1998.
[94] Liu S, Zhu S, Yu X et al. Study on chaotic parameter range of nonlinearvibration isolation system: proceedings of the Proceedings of the2004International Symposium on Safety Science and Technology, Shanghai, China,2004[C].
[95] Liu S, Yu X, Zhu S. Study on the chaos anti-control technology in nonlinearvibration isolation system[J]. Journal of sound and vibration,2008,310(4-5):855-864.
[96] Lou JJ, Zhu SJ, He L et al. Experimental chaos in nonlinear vibration isolationsystem[J]. Chaos, Solitons&Fractals,2009,40(3):1367-1375.
[97]陈予恕.非线性振动系统的分叉和混沌理论[M].北京:高等教育出版社,1993
[98]刘延柱.非线性振动[M].北京:高等教育出版社,2001.
[99]陈予恕.非线性振动[M].北京:高等教育出版社,2002.
[100]楼京俊,朱石坚,何琳. Duffing系统对称破缺分岔及其逆分岔研究[J].武汉理工大学学报:交通科学与工程版,2005,29(1):45-48.
[101]Chen A, Lü J, Yu S. Generating hyperchaotic Lü attractor via state feedbackcontrol[J]. Physica A: Statistical Mechanics and its Applications,2006,364:103-110.
[102]刘秉正,彭建华.非线性动力学[M].北京:高等教育出版社,2004.
[103]Chow SN, Hale JK. Methods of bifurcation theory[M]. Springer New York,1996.
[104]Haken H. Advanced synergetics: Instability hierarchies of self-organizingsystems and devices[M]. Springer-verlag Berlin,1983.
[105]俞翔,朱石坚.硬刚度特性非线性隔振系统分叉的数值研究[J].噪声与振动控制,2003,23(005):5-9.
[106]俞翔,朱石坚,刘树勇.多自由度非线性隔振系统建模及其非共振响应[J].振动与冲击,2007,26(7):69-73.
[107]俞翔,朱石坚,刘树勇.广义混沌同步中的多稳定同步流形[J].物理学报,2008,57(5).
[108]俞翔. PMUCR方法在高维非线性动力学系统中的应用[J].应用力学学报,2006,23.
[109]Yu X, Zhu S, Liu S. Study on the performance of nonlinear vbration-isolationsystem under chaotic state[J]. Progress in Safety Science and Technology,Shanghai, China,2004:1417-1421.
[110]楼京俊,何其伟,朱石坚.多频激励软弹簧型Duffing系统中的混沌[J].应用数学和力学,2004,25(012):1299-1304.
[111]俞翔,刘树勇,朱石坚.非线性隔振系统混沌特性实验研究[J].噪声与振动控制,2003,23(004):9-11.
[112]Yu X., Zhu S.J., Liu Y.S. et al. Study on performance of nonlinear vibrationisolation under chaotic state[J]. Proceedings of the International Symposium onSafety Science and Technology, Shanghai, China,2004,4:1417–1421.
[113]俞翔.硬刚度特性非线性隔振系统分叉的数值研究[J].噪声与振动控制,2003,23.
[114]楼京俊.混沌隔振方法研究[J].船舶力学,2006,10.
[115]徐伟,何琳,吕志强等.船舶主机气囊隔振系统动态特性分析[J].振动与冲击,2007,26(7).
[116]楼京俊,何其伟,朱石坚.多频激励软弹簧型Dufing系统中的混沌[J].应用数学和力学,2004,25(12).
[117]姜荣俊,朱石坚,翁雪涛.混沌状态下非线性隔振装置的隔振性能评估[J].机械强度,2003,25(1):025～027.
[118]朱石坚.基于Lyapunov指数谱的非线性隔振系统混沌运动参数区域预测[J].海军工程大学学报,2003,15.
[119]Wen G, Xu D. Nonlinear observer control for full-state projectivesynchronization in chaotic continuous-time systems[J]. Chaos, Solitons&Fractals,2005,26(1):71-77.
[120]Wang XF, Chen GR. On feedback anticontrol of discrete chaos[J]. InternationalJournal of Bifurcation and Chaos,1999,9(7):1435–1441.
[121]Wang XF, Chen GR. Chaotification via arbitrarily small feedback controls:theory, method, and applications[J]. International Journal of Bifurcation andChaos,2000,10(3):549–570.
[122]Zhong GQ, Man KF, Chen GR. Generating chaos via a dynamical controller[J].International Journal of Bifurcation and Chaos,2001,11(3):865–869.
[123]Tang KS, Man KF, Zhong GQ et al. Generating chaos via x|x|[J]. IEEETransactions on Circuits and Systems,2001,48(5):636–641.
[124]Konishi K. Making chaotic behavior in a damped linear harmonic oscillator[J].Physics Letters A,2001,284(2-3):85-90.
[125]Konishi K. Generating chaotic behavior in an oscillator driven by periodicforces[J]. Physics Letters A,2003,320(2-3):200-206.
[126]Yang L, Liu Z, Chen G. Chaotifying a continuous-time system via impulsiveinput[J]. International Journal of Bifurcation and Chaos,2002,12(5):1121–1128.
[127]Wen G, Lu Y, Zhang Z et al. Line spectra reduction and vibration isolation viamodified projective synchronization for acoustic stealth of submarines[J].Journal of sound and vibration,2009,324(3-5):954-961.
[128]Hu HY, Wang ZH. Stability analysis of damped sdof systems with two timedelays in state feedback[J]. Journal of sound and vibration,1998,214(2):213-225.
[129]Xu J, Chung KW. Effects of time delayed position feedback on a van derPol-Duffing oscillator[J]. Physica D: Nonlinear Phenomena,2003,180(1-2):17-39.
[130]Chen G, Lai D. Feedback control of Lyapunov exponents for discrete-timedynamical systems[J]. International Journal of Bifurcation and Chaos in AppliedSciences and Engineering,1996,6(7):1341-1350.
[131]Wang XF, Chen G. Generating topologically conjugate chaotic systems viafeedback control[J]. Circuits and Systems I: Fundamental Theory andApplications, IEEE Transactions on,2003,50(6):812-817.
[132]Wang X. Generating chaos in continuous-time systems via feedback control[J].Chaos Control,2003:179-204.
[133]关新平,范正平,张群亮等.连续时间稳定线性系统的混沌反控制研究[J].物理学报,2002,51(10):2216-2220.
[134]任海鹏,刘丁.基于非线性跟踪的混沌反控制[J].系统仿真学报,2005,17(2):432-434.
[135]Chen L-Q, Zhang N-H, Zu JW. The regular and chaotic vibrations of an axiallymoving viscoelastic string based on fourth order Galerkin truncaton[J]. Journalof sound and vibration,2003,261(4):764-773.
[136]Chen HK, Lee CI. Anti-control of chaos in rigid body motion[J]. Chaos, Solitonsand Fractals,2004,21:957–965.
[137]Ge ZM, Chang CM, Chen YS. Anti-control of chaos of single time scalebrushless dc motors and chaos synchronization of different order systems[J].Chaos, Solitons and Fractals,2006,27:1298–1315.
[138]Ge ZM, Zhang AR. Anticontrol of chaos of the fractional order modified van derPol systems[J]. Applied mathematics and computation,2007,187(2):1161-1172.
[139]Ge ZM, Leu WY. Anti-control of chaos of two-degrees-of-freedom loudspeakersystem and chaos synchronization of different order systems[J]. Chaos, Solitons&Fractals,2004,20(3):503-521.
[140]Wang H, Han Z, Zhang W et al. Chaos control and synchronization of unifiedchaotic systems via linear control[J]. Journal of sound and vibration,2009,320(1-2):365-372.
[141]Ge ZM, Yang CH. Chaos synchronization and chaotization of complex chaoticsystems in series form by optimal control[J]. Chaos, Solitons&Fractals,2009,42(2):994-1002.
[142]黄玮,张化光,王智良.基于采样数据二维连续线性系统的混沌反控制[J].吉林大学学报:信息科学版,2004,22(004):323-326.
[143]朱海磊,陈基和,王赞基.利用延迟反馈进行异步电动机混沌反控制[J].中国电机工程学报,2004,24(12):175-178.
[144]孟昭军,孙昌志.一类永磁电动机的混沌反控制研究[J].自动化技术与应用,2006,25(008):7-9.
[145]张卓,李忠.永磁同步电动机混沌系统的反控制[J].暨南大学学报:自然科学与医学版,2001,22(003):44-46.
[146]李俊,陈基和,邹国棠.永磁直流电机的混沌反控制[J].中国电机工程学报,2006,26(8):77-81.
[147]Chacon R. Maintenance and suppression of chaos by weak harmonicperturbations: a unified view[J]. Physical Review Letters,2001,86(9):1737-1740.
[148]Chan WC, Tes CK. What form of control function can drive adiscontinuous-mode boost converter to chaos via period-doubling[J].International Journal of Circuit Theory and Applications,1998,26:281-286.
[149]Chen G. Controlling chaos and bifurcations in engineering systems[M]. CRC,2000.
[150]Chen G, Zhou J, Hsu SB. Linear superposition of chaotic and orderly vibrationson two serially connected strings with a van der Pol joint[J]. InternationalJournal of Bifurcation and Chaos in Applied Sciences and Engineering,1996,6(8):1509-1528.
[151]Chen G, Huang T, Juang J et al. Unbounded growth of total variations ofsnapshots of the1D linear wave equation due to the chaotic behavior of iteratesof composite nonlinear boundary reflection relations[J]. LECTURE NOTES INPURE AND APPLIED MATHEMATICS,2001:15-44.
[152]Chen M, Chen Z, Chen G. Approximate solutions of operator equations[M].World Scientific Pub Co Inc,1997.
[153]Lü J, Zhou T, Chen G et al. Generating chaos with a switching piecewise-linearcontroller[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science,2002,12(2):344.
[154]Lü J, Yu X, Chen G. Generating chaotic attractors with multiple merged basins ofattraction: A switching piecewise-linear control approach[J]. Circuits andSystems I: Fundamental Theory and Applications, IEEE Transactions on,2003,50(2):198-207.
[155]Wang Z, Chau KT. Anti-control of chaos of a permanent magnet DC motorsystem for vibratory compactors[J]. Chaos, Solitons&Fractals,2008,36(3):694-708.
[156]Diekmann O. Delay equations: functional-, complex-, and nonlinear analysis[M].Springer,1995.
[157]Kuang Y. Delay differential equations: with applications in populationdynamics[M]. Academic Pr,1993.
[158]Glendinning P. Stability, instability, and chaos: An introduction to the theory ofnonlinear differential equations[M]. Cambridge Univ Pr,1994.
[159]Mensour B, Longtin A. Controlling chaos to store information indelay-differential equations[J]. Physics Letters A,1995,205(1):18-24.
[160]Lu H, He Z. Chaotic behavior in first-order autonomous continuous-time systemswith delay[J]. Circuits and Systems I: Fundamental Theory and Applications,IEEE Transactions on,1996,43(8):700-702.
[161]Celka P. Delay-differential equation versus1D-map: Application to chaoscontrol[J]. Physica D: Nonlinear Phenomena,1997,104(2):127-147.
[162]陈关荣,汪小帆.动力系统的混沌化[M].上海:上海交通大学出版社,2006.
[163]任海鹏,刘丁,韩崇昭.基于直接延迟反馈的混沌反控制[J].物理学报,2006,55(6):2694-2698.
[164]Stépán G. Retarded Dynamical Systems: Stability and Characteristic Functions:proceedings of the Pitman Research Notes in Mathematics Series, New York,1989[C]. Longman Scientific and Technical, Wiley.
[165]秦元勋,刘永清,王联.带有时滞的动力系统的运动稳定性[M].科学出版社,1989.
[166]Hassard BD. Counting Roots of the Characteristic Equation for LinearDelay-Differential Systems[J]. Journal of Differential Equations,1997,136(2):222-235.
[167]Kolmanovski VB, Nosov VR. Stability of Functional Differential Equations[M].London: Academic Press,1986.
[168]Olgac N, Sipahi R. An exact method for the stability analysis of time-delayedlinear time-invariant systems[J]. IEEE Transactions on Automatic Control,2002,47:793–797.
[169]Faria T, Magalhaes LT. Normal forms for retarded functional differentialequations with parameters and applications to Hopf bifurcation[J]. Journal ofDifferential Equations,1995,122(2):181-200.
[170]Faria T, Magalhaes LT. Normal forms for retarded functional differentialequations and applications to Bogdanov-Takens singularity[J]. Journal ofDifferential Equations,1995,122(2):201-224.
[171]Stech HW. Hopf bifurcation calculations for functional differential equations[J].J MATH ANAL APPLIC,1985,109(2):471-491.
[172]Hu H, Dowell EH, Virgin LN. Resonances of a harmonically forced Duffingoscillator with time delay state feedback[J]. Nonlinear Dynamics,1998,15(4):311-327.
[173]Wang XF, Chen G, Yu X. Anticontrol of chaos in continuous-time systems viatime-delay feedback[J]. Chaos: An Interdisciplinary Journal of NonlinearScience,2000,10(4):771-779.
[174]Wang XF, Chen G. Chaotifying a stable LTI system by tiny feedback control[J].Circuits and Systems I: Fundamental Theory and Applications, IEEETransactions on,2000,47(3):410-415.
[175]Wang XF, Zhong GQ, Tang KS et al. Generating chaos in Chua's circuit viatime-delay feedback[J]. Circuits and Systems I: Fundamental Theory andApplications, IEEE Transactions on,2001,48(9):1151-1156.
[176]Wang XF, Chen GR, Man KF. Making a continuous-time minimum phase systemchaotic by time-delay feedback[J]. IEEE Transactions on Circuit and Systems,2001,48(5):641–645.
[177]Hu HY, Wang ZH. Dynamics of Controlled Mechanical Systems with DelayedFeedback[M]. Heidelberg: Springer,2002.
[178]Zhao YH. Stability of a two-dimensional airfoil with time-delayed feedbackcontrol[J]. Journal of Fluids and Structures,2009,25(1):1-25.
[179]Zhou J, Xu D, Li Y. Chaotifing Duffing-type System with Large ParameterRange Based on Optimal Time-Delay Feedback Control: proceedings of theProceedings of2010International Workshop on Chaos-Fractal Theories andApplications, Kunming, Yunnan, China, October29-31,2010[C].
[180]Heiden Uad, Walther HO. Existence of chaos in control system with delayedfeedback[J]. Journal of Differential Equations,1983,47:273-295.
[181]Tsuda Y, Tamura H, Sueoka A et al. Chaotic behaviour of a nonlinear vibratingsystem with a retarded argument[J]. JSME international journal Ser3, Vibration,control engineering, engineering for industry,1992,35(2):259-267.
[182]Chen JH. Controlling chaos and chaotification in the Chen-Lee system bymultiple time delays[J]. Chaos, Solitons&Fractals,2008,36(4):843-852.
[183]Zhao YY, Xu J. Effects of delayed feedback control on nonlinear vibrationabsorber system[J]. Journal of sound and vibration,2007,308(1-2):212-230.
[184]Li X, Ji JC, Hansen CH. Dynamics of two delay coupled van der Poloscillators[J]. Mechanics Research Communications,2006,33(5):614-627.
[185]Qian CZ, Tang JS. A time delay control for a nonlinear dynamic beam undermoving load[J]. Journal of sound and vibration,2008,309(1-2):1-8.
[186]De Paula AS, Savi MA. Controlling chaos in a nonlinear pendulum using anextended time-delayed feedback control method[J]. Chaos, Solitons&Fractals,2009,42(5):2981-2988.
[187]Cao J, Ho DWC, Yang Y. Projective synchronization of a class of delayedchaotic systems via impulsive control[J]. Physics Letters A,2009,373(35):3128-3133.
[188]Ding D, Zhu J, Luo X et al. Controlling Hopf Bifurcation in Fluid Flow Model ofInternet Congestion Control System[J]. International Journal of Bifurcation andChaos,2009,19(4):1415.
[189]Jin M, Chang PH. Simple robust technique using time delay estimation for thecontrol and synchronization of Lorenz systems[J]. Chaos, Solitons&Fractals,2009,41(5):2672-2680.
[190]Wang M, Wang X. Controlling Liu System with Different Methods[J]. ModernPhysics Letters B,2009,23(14):1805-1818.
[191]Li L, Peng H, Yang Y et al. On the chaotic synchronization of Lorenz systemswith time-varying lags[J]. Chaos, Solitons&Fractals,2009,41(2):783-794.
[192]Sen A, Mukherjee D. Chaos in the delay logistic equation with discontinuousdelays[J]. Chaos, Solitons&Fractals,2009,40(5):2126-2132.
[193]Miao Q, Tang Y, Lu S et al. Lag synchronization of a class of chaotic systemswith unknown parameters[J]. Nonlinear Dynamics,2009,57(1):107-112.
[194]Inarrea M. Chaos and its control in the pitch motion of an asymmetric magneticspacecraft in polar elliptic orbit[J]. Chaos, Solitons&Fractals,2009,40(4):1637-1652.
[195]Hu HY, Wang ZH. Singular perturbation methods for nonlinear dynamic systemswith time delays[J]. Chaos, Solitons&Fractals,2009,40(1):13-27.
[196]Xu J, Chung KW. Dynamics for a class of nonlinear systems with time delay[J].Chaos, Solitons&Fractals,2009,40(1):28-49.
[197]Chen LX, Cai GP, Pan J. Experimental study of delayed feedback control for aflexible plate[J]. Journal of sound and vibration,2009,322(4-5):629-651.
[198]Li T, Yu J, Wang Z. Delay-range-dependent synchronization criterion for Lur'esystems with delay feedback control[J]. Communications in Nonlinear Scienceand Numerical Simulation,2009,14(5):1796-1803.
[199]Vasegh N, Khaki Sedigh A. Chaos control via TDFC in time-delayed systems:The harmonic balance approach[J]. Physics Letters A,2009,373(3):354-358.
[200]Zhong H, Guo Q. Nonlinear vibration analysis of Timoshenko beams using thedifferential quadrature method[J]. Nonlinear Dynamics,2003,32(3):223-234.
[201]Howard CQ. A new cost function algorithm for adaptive-passive vibration andacoustic resonators[J]. Proceedings of Acoustics2011:2-4.
[202]Choi SB, Sohn JW, Choi SM et al. A piezostack-based active mount forbroadband frequency vibration control: experimental validation[J]. SmartMaterials and Structures,2009,18:097001.
[203]Dylejko PG, Kessissoglou NJ, Tso Y et al. Optimisation of a resonance changerto minimise the vibration transmission in marine vessels[J]. Journal of sound andvibration,2007,300(1-2):101-116.
[204]Caresta M, Kessissoglou NJ. Reduction of Hull-Radiated Noise UsingVibroacoustic Optimization of the Propulsion System[J]. Journal of ShipResearch,55(3):149-162.
[205]Howard CQ, Craig RA. Adaptive-Passive Quarter-Wave Tube Resonator Silencer:proceedings of the Proceedings of Acoustics2011: Annual conference of theAustralian Acoustical Society,2011[C].
[206]Chu SY, Soong TT, Lin CC et al. Time delay effect and compensation on directoutput feedback controlled mass damper systems[J]. Earthquake engineering&structural dynamics,2002,31(1):121-137.
[207]Fofana MS. Sufficient conditions for the stability of single and multipleregenerative chatter[J]. Chaos, Solitons&Fractals,2002,14(2):335-347.
[208]Gouskov AM, Voronov SA, Paris H et al. Nonlinear dynamics of a machiningsystem with two interdependent delays[J]. Communications in Nonlinear Scienceand Numerical Simulation,2002,7(4):207-221.
[209]Fofana MS. Delay dynamical systems and applications to nonlinear machine-toolchatter[J]. Chaos, Solitons&Fractals,2003,17(4):731-747.
[210]Zervas E. Comparative study of some experimental methods to characterize thecombustion process in a SI engine[J]. Energy,2005,30(10):1803-1816.
[211]Librescu L, Marzocca P, Silva WA. Aeroelasticity of2-D lifting surfaces withtime-delayed feedback control[J]. Journal of Fluids and Structures,2005,20(2):197-215.
[212]Li C, Liao X, Wong K. Chaotic lag synchronization of coupled time-delayedsystems and its applications in secure communication[J]. Physica D: NonlinearPhenomena,2004,194(3-4):187-202.
[213]Geng L, Osusky K, Konjeti S et al. Radiation-guided drug delivery to tumorblood vessels results in improved tumor growth delay[J]. Journal of controlledrelease,2004,99(3):369-381.
[214]Toth-Fejel SE, Pommier RF. Relationships among delay of diagnosis, extent ofdisease, and survival in patients with abdominal carcinoid tumors[J]. TheAmerican journal of surgery,2004,187(5):575-579.
[215]Routh EJ. A Treatise on the Stability of a Given State of Motion[M]. London:Macmillan1877.
[216]Hurwitz A. On the conditions under which an equation has only roots withnegative real parts[J]. Mathematicsche Annelen,1895,46:273-284.
[217]Forde J, Nelson P. Applications of Sturm sequences to bifurcation analysis ofdelay differential equation models[J]. Journal of Mathematical Analysis andApplications,2004,300(2):273-284.
[218]Wang ZH, Hu HY. Stability switches of time-delayed dynamic systems withunknown parameters[J]. Journal of sound and vibration,2000,233(2):215-233.
[219]Zhou J, Xu D, Li Y. Chaotifing duffing-type system with large parameter rangebased on optimal time-delay feedback control: proceedings of. IEEE.
[220]Nayfeh AH. Perturbation methods[M]. Wiley Online Library,1973.
[221]Kevorkian J, Cole JD. Multiple scale and singular perturbation methods[M].Springer Verlag,1996.
[222]Oueini SS, Nayfeh HA. Single-mode control of a cantilever beam under principalparametric excitation[J]. Journal of sound and vibration,1999,224(1):33-47.
[223]Wirkus S, Rand R. The dynamics of two coupled van der Pol oscillators withdelay coupling[J]. Nonlinear Dynamics,2002,30(3):205-221.
[224]Zhou J, Xu D, Li Y. An active-passive nonlinear vibration isolation method basedon optimal time-delay feedback control[J]. Journal of Vibration Engineering,2011: On press.
[225]Li YL, Xu DL, Fu YM et al. Stability and chaotification of vibration isolationfloating raft systems with time-delayed feedback control[J]. Chaos (Woodbury,NY),21(3):033115.
[226]Zhang J, Xu D, Zhou J et al. Chaotification of vibration isolation floating raftsystem via nonlinear time-delay feedback control[J]. Chaos, Solitons&Fractals,2012,45(9):1255-1265.
[227]Chen G, Wang X. Chaotification of dynamics system: theory, method andapplication[M]. Shanghai: Shanghai Jiao Tong University Press,2006.
[228]Zhou J, Xu D, Zhang J et al. Spectrum optimization-based chaotification usingtime-delay feedback control[J]. Chaos, Solitons&Fractals,2012,45:815-824.
[229]Zhou J, Xu D, Li Y. An active-passive nonlinear vibration isolation method basedon optimal time-delay feedback control[J]. Journal of Vibration Engineering,2011,24(6):639-645.
[2]朱英富,张国良.舰船隐身技术[M].哈尔滨:哈尔滨工程大学出版社,2003.
[3]孟晓宇,肖国林,陈虹.国外潜艇声隐身技术现状与发展综述[J].舰船科学技术,33(11):135-139.
[4]郑兆宁,向大威.水声信号被动检测与参数估计理论[M].北京:科学出版社,1983.
[5] Snowdon JC. Vibration isolation: use and characterization[J]. The Journal of theAcoustical Society of America,1979,66(5):1245-1274.
[6] Howard CQ. Recent Developments in Submarine Vibration Isolation and NoiseControl: proceedings of the Conference2011Presentations&Proceedings onUSB,2011[C].
[7]马运义,黄白,伏同先.船舶振动控制[M].大连,1992.
[8]丁文镜.减振理论[M].北京:清华大学出版社,1988.
[9]朱石坚,楼京俊,何其伟.振动理论与隔振技术[M].北京:国防工业出版社,2006.
[10] Nayfeh TA, Emaci E, Vakakis AF. Application of nonlinear localization to theoptimization of a vibration isolation system[J]. AIAA journal,1997,35(8):1378-1386.
[11] Ibrahim RA. Recent advances in nonlinear passive vibration isolators[J]. Journalof sound and vibration,2008,314(3-5):371-452.
[12] Fidlin A. Nonlinear oscillations in mechanical engineering[M]. Springer Verlag,2006.
[13] Zhang JZ, Li DD, Shen D. Study on Euler spring used in ultra–low frequencyvertical vibration isolation system[J]. Journal of Mechanical Strength,2004,3(26):237–241.
[14] Vakakis AF, Manevitch LI, Gendelman O et al. Dynamics of linear discretesystems connected to local, essentially non-linear attachments[J]. Journal ofsound and vibration,2003,264(3):559-577.
[15] Zhang JZ, Li D, Chen MJ et al. An ultra-low frequency parallel connectionnonlinear isolator for precision instruments[J]. Key Engineering Materials,2004,257:231-238.
[16] Casati G, Ford J, Casati G et al. Stochastic behavior in classical and quantumhamiltonian systems[M]. Springer-Verlag,1979.
[17] Li TY, Yorke JA. Period three implies chaos[J]. The American MathematicalMonthly,1975,82(10):985-992.
[18]陈式刚.映象与混沌[M].北京:国防工业出版社,1992.
[19]郝柏林.从抛物线谈起-混沌动力学引论[M].上海:上海科技教育出版社,1993.
[20]钱伟长.非线性力学的新发展-稳定性、分叉、突变、浑沌[M].武汉:华中理工大学出版社,1988.
[21]胡岗.随机力与非线性系统[M].上海:上海科技教育出版社,1994.
[22]郝柏林.分岔、混沌、奇怪吸引子、湍流及其他[J].物理学进展,1983,3(3):329-416.
[23]龙运佳,王聪玲,张平.基于混沌理论的振动压路机[J].中国农业大学学报,1998,3(002):19-22.
[24]龙运佳,杨勇.重型自行式混沌振动压路机[J].中国农业大学学报,2000,5(002):12-14.
[25] Lou JJ, Zhu SJ, He L et al. Application of chaos method to line spectrareduction[J]. Journal of sound and vibration,2005,286(3):645-652.
[26]朱石坚.线谱激励的混沌隔振研究[J].海军工程大学学报,2003,15.
[27] Jiang RJ, Zhu SJ. Vibration isolation and chaotic vibration: proceedings of theProceedings of the ASME International Design Engineering TechnicalConferences and Computers and Information in Engineering Conference－DETC2005, Chicago,2005[C]. ASME.
[28] Zhu SJ, Zheng YF, Fu YM. Analysis of non-linear dynamics of atwo-degree-of-freedom vibration system with non-linear damping and non-linearspring[J]. Journal of sound and vibration,2004,271(1-2):15-24.
[29]楼京俊,朱石坚.混沌隔振方法研究[J].船舶力学,2007,10(5):135-141.
[30] Jing-jun L, Qi-wei H, Shi-jian Z. Chaos in the softening duffing system undermulti-frequency periodic forces[J]. Applied Mathematics and Mechanics,2004,25(12):1421-1427.
[31] He QW, Zhu SJ, Lou JJ. Study on the computation method of piecewise linearsystem[J]. Dynamics of Continuous，Discrete，Impulsive Systems–Series A–Mathematical Analysis,2006,13:1400–1404.
[32] Yu X, Zhu S, Liu S. A new method for line spectra reduction similar togeneralized synchronization of chaos[J]. Journal of sound and vibration,2007,306(3-5):835-848.
[33]何琳,姚耀中.潜艇声隐身技术研究进展[J].舰船科学技术,2007,29(5):29-43.
[34]王国治.浮筏隔振装置抗基础冲击的研究[J].噪声与振动控制,2000,(6):10-13.
[35]赵应龙,何琳,吕志强.应用DDAM进行船舶浮筏隔振装置抗冲击计算[J].工程力学,2007,24(4):159-167.
[36]束立红,胡宗成,吕志强.国外舰船隔振器研究进展[J].舰船科学技术,2006,28(003):109-112.
[37]戴德沛.阻尼技术的工程应用[M].清华大学出版社,1991.
[38]张平宽.薄膜阻尼技术在电冰箱压缩机噪声控制中的应用[J].哈尔滨理工大学学报,1998,3(002):40-42.
[39]何琳.潜艇声隐身技术进展[J].舰船科学技术,2007,29(5):9-17.
[40]郭日修,朱云翔.船舶防振减振技术的进展[J].振动与冲击,1993,12(003):36-48.
[41]吴广明,沈荣瀛,李俊等.多层隔振系统的动力学模型[J].振动与冲击,2005,24(002):16-20.
[42]贺华,冯奇.双层隔振系统动力学建模和响应计算[J].同济大学学报:自然科学版,2004,32(012):1578-1582.
[43]王志刚,冯奇,汪玉.弹性浮筏系统动力学建模及冲击响应分析[J].船舶力学,2005,9(006):113-125.
[44]束立红,胡宗成,吕志强.国外舰船隔振器研究进展[J].舰船科学技术,2006,28(23).
[45] Kim S, Singh R. Vibration transmission through an isolator modelled bycontinuous system theory[J]. Journal of sound and vibration,2001,248(5):925-953.
[46]吕志强,黄映云,赵应龙等.浮筏隔振装置设计中的模态控制研究[J].振动工程学报,2004,17.
[47]陈安华,高威,高永毅.被动隔振的非线性动力学研究[J].中国机械工程,2008,19(9).
[48] Yu X, Zhu SJ, Liu SY. Bifurcation and chaos in multi-degree-of-freedomnonlinear vibration isolation system[J]. Chaos, Solitons&Fractals,2008,38(5):1498-1504.
[49]俞翔,姜荣俊,朱石坚.非线性隔振系统周期解的全局性态分析: proceedingsof the2002年全国振动工程及应用学术会议论文,北京,2002[C].
[50] Yu X., Zhu S., Lou J. Bifurcation analysis of nonlinear vibration isolation withhard stiffness by cell mapping[J]. Proceedings of the ASME Design EngineeringTechnical Conference on Mechanical Vibration and Noise, Chicago, IL, USA,2003,5B:1615–1619.
[51] Zhou Y. F., Tang J. Y., H. HX. Response and transmissibility of strong nonlinearactive isolation system[J]. Journal of Central South University (Science andTechnology),2005,36:496–500.
[52]姜荣俊.混沌隔振装置的设计[J].海军工程大学学报,2003,15.
[53]张磊,付永领,刘永光等.主动隔振技术及其应用与发展[J].机床与液压,2005,(002):5-8.
[54]杨铁军,靳国永,李玩幽等.舰船动力装置振动主动控制技术研究[J].舰船科学技术,2006,(0z2):46-53.
[55]顾仲权,马扣根,陈卫东等.振动主动控制[M].国防工业出版社,1997.
[56]贾玉红,王建军.飞机起落架的主动控制与半主动控制研究[J].兵工学报,2006,27(003):528-532.
[57]胡海岩,郭大蕾.振动半主动控制技术的进展[J].振动测试与诊断,2001,21(4):235-244.
[58]王加春,李旦.机械振动主动控制技术的研究现状和发展综述[J].机械强度,2001,23(2):156-160.
[59]徐洋,华宏星,张志谊等.舰船主动隔振技术综述[J].舰船科学技术,2009,30(2):27-33.
[60]周临震,刘德仿.电动式激振器骨架的形状优化设计[J].机械工程师,2006,(003):61-63.
[61]张洪田,李玩幽.电动式主动吸振技术研究[J].振动工程学报,2001,14(001):113-117.
[62]张磊,束立红,刘永光等.基于CMAC网络的主动隔振控制技术[J].机械科学与技术,2006,25(10):1160-1162.
[63]张磊,刘永光,付永领等.基于磁致伸缩作动器的主动隔振系统分析[J].航空动力学报,2005,19(6):782-785.
[64]夏兆旺,杨绍普,金宝宁等.基于磁流变液的半主动控制研究[J].现代机械,2005,(006):25-26.
[65]王炅,黄文良.磁流变减振器在半主动振动控制中的应用[J].南京理工大学学报:自然科学版,2004,28(3):269-272.
[66] Howard CQ. Technologies for the Management of the Acoustic Signature of aSubmarine: proceedings of the Proceedings of the Submarine Institute ofAustralia2010: SIA5th Biennial Conference,2010[C].
[67] Drathen AV. Propulsion system solutions for present and future naval vessels:proceedings of the Pacific, Sydney, Australia,27-29January,2010[C].
[68]束立红,范名琦.基于磁致伸缩作动器的主动隔振实验研究[J].振动与冲击,2006,25(5).
[69]陈士华,陆君安.混沌动力学初步[M].武汉水利电力大学出版社,1998.
[70]刘增荣.混沌的微扰判据[M].上海:上海科技教育出版社.1994.
[71] Ott E. Chaos in dynamical systems[M]. Cambridge Univ Pr,2002.
[72] Lorenz EN. Deterministic nonperiodic flow[J]. Journal of the atmosphericsciences,1963,20(2):130-141.
[73]龙运佳.混沌振动研究[J].方法与实践北京:清华大学出版社,1997,4.
[74]吴祥兴,陈忠.混沌学导论[M].上海科学技术文献出版社,1996.
[75]张琪昌,王洪礼,竺致文.分岔与混沌理论及应用[M].天津大学出版社,2005.
[76]舒仲周,张继业,曹登庆.运动稳定性[M].中国铁道出版社,2001.
[77]王洪礼,张琪昌,郭树起.非线性动力学理论及其应用[M].天津科学技术出版社,2002.
[78] Bondaryk JE. Vibration of truss structures[J]. The Journal of the AcousticalSociety of America,1997,102:2167.
[79] Steliana C. Desynchronization and chaotification of nonlinear dynamicalsystems[J]. Chaos, Solitons and Fractals,2005,24:1307–1315.
[80] Chen HK, Lin TN, Chen JH. Dynamic analysis, controlling chaos andchaotification of a SMIB power system[J]. Chaos, Solitons and Fractals,2005,24:1307–1315.
[81] Mohamed Z, Ahmed O, Nejib S. Controlling chaos in the permanent magnetsynchronous motor[J]. Chaos, Solitons and Fractals,2009,41:1266–1276.
[82] Chen HK, Ge ZM. Bifurcations and chaos of a two-degree-of-freedomdissipative gyroscope[J]. Chaos, Solitons&Fractals,2005,24(1):125-136.
[83] Ge ZM, Cheng JW, Chen YS. Chaos anticontrol and synchronization of threetime scales brushless DC motor system[J]. Chaos, Solitons&Fractals,2004,22(5):1165-1182.
[84] Moukam Kakmeni FM, Bowong S, Tchawoua C et al. Chaos control andsynchronization of a Φ6-Van der Pol oscillator[J]. Physics Letters A,2004,322(5):305-323.
[85] Carrella A, Brennan MJ, Waters TP et al. On the design of ahigh-static-low-dynamic stiffness isolator using linear mechanical springs andmagnets[J]. Journal of sound and vibration,2008,315(3):712-720.
[86] Eissa M, Bauomy HS, Amer YA. Active control of an aircraft tail subject toharmonic excitation[J]. Acta Mechanica Sinica,2007,23(4):451-462.
[87] Sheu LJ, Chen HK, Chen JH et al. Chaotic dynamics of the fractionally dampedDuffing equation[J]. Chaos, Solitons&Fractals,2007,32(4):1459-1468.
[88] Lee CM, Goverdovskiy VN, Temnikov AI. Design of springs with "negative"stiffness to improve vehicle driver vibration isolation[J]. Journal of sound andvibration,2007,302(4):865-874.
[89] Jing XJ, Lang ZQ. Frequency domain analysis of a dimensionless cubicnonlinear damping system subject to harmonic input[J]. Nonlinear Dynamics,2009,58(3):469-485.
[90] Yassen MT. Chaos control of chaotic dynamical systems using backsteppingdesign[J]. Chaos, Solitons&Fractals,2006,27(2):537-548.
[91]胡岗,萧井华,郑志刚.混沌控制[M].上海:上海科技教育出版社,2000.
[92]王光瑞,陈式刚.混沌的控制、同步与应用[M].北京:国防工业出版社,2001.
[93] Chen G, Dong X. From chaos to order: methodologies, perspectives andapplications[M]. Singapore: World Scientific,1998.
[94] Liu S, Zhu S, Yu X et al. Study on chaotic parameter range of nonlinearvibration isolation system: proceedings of the Proceedings of the2004International Symposium on Safety Science and Technology, Shanghai, China,2004[C].
[95] Liu S, Yu X, Zhu S. Study on the chaos anti-control technology in nonlinearvibration isolation system[J]. Journal of sound and vibration,2008,310(4-5):855-864.
[96] Lou JJ, Zhu SJ, He L et al. Experimental chaos in nonlinear vibration isolationsystem[J]. Chaos, Solitons&Fractals,2009,40(3):1367-1375.
[97]陈予恕.非线性振动系统的分叉和混沌理论[M].北京:高等教育出版社,1993
[98]刘延柱.非线性振动[M].北京:高等教育出版社,2001.
[99]陈予恕.非线性振动[M].北京:高等教育出版社,2002.
[100]楼京俊,朱石坚,何琳. Duffing系统对称破缺分岔及其逆分岔研究[J].武汉理工大学学报:交通科学与工程版,2005,29(1):45-48.
[101]Chen A, Lü J, Yu S. Generating hyperchaotic Lü attractor via state feedbackcontrol[J]. Physica A: Statistical Mechanics and its Applications,2006,364:103-110.
[102]刘秉正,彭建华.非线性动力学[M].北京:高等教育出版社,2004.
[103]Chow SN, Hale JK. Methods of bifurcation theory[M]. Springer New York,1996.
[104]Haken H. Advanced synergetics: Instability hierarchies of self-organizingsystems and devices[M]. Springer-verlag Berlin,1983.
[105]俞翔,朱石坚.硬刚度特性非线性隔振系统分叉的数值研究[J].噪声与振动控制,2003,23(005):5-9.
[106]俞翔,朱石坚,刘树勇.多自由度非线性隔振系统建模及其非共振响应[J].振动与冲击,2007,26(7):69-73.
[107]俞翔,朱石坚,刘树勇.广义混沌同步中的多稳定同步流形[J].物理学报,2008,57(5).
[108]俞翔. PMUCR方法在高维非线性动力学系统中的应用[J].应用力学学报,2006,23.
[109]Yu X, Zhu S, Liu S. Study on the performance of nonlinear vbration-isolationsystem under chaotic state[J]. Progress in Safety Science and Technology,Shanghai, China,2004:1417-1421.
[110]楼京俊,何其伟,朱石坚.多频激励软弹簧型Duffing系统中的混沌[J].应用数学和力学,2004,25(012):1299-1304.
[111]俞翔,刘树勇,朱石坚.非线性隔振系统混沌特性实验研究[J].噪声与振动控制,2003,23(004):9-11.
[112]Yu X., Zhu S.J., Liu Y.S. et al. Study on performance of nonlinear vibrationisolation under chaotic state[J]. Proceedings of the International Symposium onSafety Science and Technology, Shanghai, China,2004,4:1417–1421.
[113]俞翔.硬刚度特性非线性隔振系统分叉的数值研究[J].噪声与振动控制,2003,23.
[114]楼京俊.混沌隔振方法研究[J].船舶力学,2006,10.
[115]徐伟,何琳,吕志强等.船舶主机气囊隔振系统动态特性分析[J].振动与冲击,2007,26(7).
[116]楼京俊,何其伟,朱石坚.多频激励软弹簧型Dufing系统中的混沌[J].应用数学和力学,2004,25(12).
[117]姜荣俊,朱石坚,翁雪涛.混沌状态下非线性隔振装置的隔振性能评估[J].机械强度,2003,25(1):025～027.
[118]朱石坚.基于Lyapunov指数谱的非线性隔振系统混沌运动参数区域预测[J].海军工程大学学报,2003,15.
[119]Wen G, Xu D. Nonlinear observer control for full-state projectivesynchronization in chaotic continuous-time systems[J]. Chaos, Solitons&Fractals,2005,26(1):71-77.
[120]Wang XF, Chen GR. On feedback anticontrol of discrete chaos[J]. InternationalJournal of Bifurcation and Chaos,1999,9(7):1435–1441.
[121]Wang XF, Chen GR. Chaotification via arbitrarily small feedback controls:theory, method, and applications[J]. International Journal of Bifurcation andChaos,2000,10(3):549–570.
[122]Zhong GQ, Man KF, Chen GR. Generating chaos via a dynamical controller[J].International Journal of Bifurcation and Chaos,2001,11(3):865–869.
[123]Tang KS, Man KF, Zhong GQ et al. Generating chaos via x|x|[J]. IEEETransactions on Circuits and Systems,2001,48(5):636–641.
[124]Konishi K. Making chaotic behavior in a damped linear harmonic oscillator[J].Physics Letters A,2001,284(2-3):85-90.
[125]Konishi K. Generating chaotic behavior in an oscillator driven by periodicforces[J]. Physics Letters A,2003,320(2-3):200-206.
[126]Yang L, Liu Z, Chen G. Chaotifying a continuous-time system via impulsiveinput[J]. International Journal of Bifurcation and Chaos,2002,12(5):1121–1128.
[127]Wen G, Lu Y, Zhang Z et al. Line spectra reduction and vibration isolation viamodified projective synchronization for acoustic stealth of submarines[J].Journal of sound and vibration,2009,324(3-5):954-961.
[128]Hu HY, Wang ZH. Stability analysis of damped sdof systems with two timedelays in state feedback[J]. Journal of sound and vibration,1998,214(2):213-225.
[129]Xu J, Chung KW. Effects of time delayed position feedback on a van derPol-Duffing oscillator[J]. Physica D: Nonlinear Phenomena,2003,180(1-2):17-39.
[130]Chen G, Lai D. Feedback control of Lyapunov exponents for discrete-timedynamical systems[J]. International Journal of Bifurcation and Chaos in AppliedSciences and Engineering,1996,6(7):1341-1350.
[131]Wang XF, Chen G. Generating topologically conjugate chaotic systems viafeedback control[J]. Circuits and Systems I: Fundamental Theory andApplications, IEEE Transactions on,2003,50(6):812-817.
[132]Wang X. Generating chaos in continuous-time systems via feedback control[J].Chaos Control,2003:179-204.
[133]关新平,范正平,张群亮等.连续时间稳定线性系统的混沌反控制研究[J].物理学报,2002,51(10):2216-2220.
[134]任海鹏,刘丁.基于非线性跟踪的混沌反控制[J].系统仿真学报,2005,17(2):432-434.
[135]Chen L-Q, Zhang N-H, Zu JW. The regular and chaotic vibrations of an axiallymoving viscoelastic string based on fourth order Galerkin truncaton[J]. Journalof sound and vibration,2003,261(4):764-773.
[136]Chen HK, Lee CI. Anti-control of chaos in rigid body motion[J]. Chaos, Solitonsand Fractals,2004,21:957–965.
[137]Ge ZM, Chang CM, Chen YS. Anti-control of chaos of single time scalebrushless dc motors and chaos synchronization of different order systems[J].Chaos, Solitons and Fractals,2006,27:1298–1315.
[138]Ge ZM, Zhang AR. Anticontrol of chaos of the fractional order modified van derPol systems[J]. Applied mathematics and computation,2007,187(2):1161-1172.
[139]Ge ZM, Leu WY. Anti-control of chaos of two-degrees-of-freedom loudspeakersystem and chaos synchronization of different order systems[J]. Chaos, Solitons&Fractals,2004,20(3):503-521.
[140]Wang H, Han Z, Zhang W et al. Chaos control and synchronization of unifiedchaotic systems via linear control[J]. Journal of sound and vibration,2009,320(1-2):365-372.
[141]Ge ZM, Yang CH. Chaos synchronization and chaotization of complex chaoticsystems in series form by optimal control[J]. Chaos, Solitons&Fractals,2009,42(2):994-1002.
[142]黄玮,张化光,王智良.基于采样数据二维连续线性系统的混沌反控制[J].吉林大学学报:信息科学版,2004,22(004):323-326.
[143]朱海磊,陈基和,王赞基.利用延迟反馈进行异步电动机混沌反控制[J].中国电机工程学报,2004,24(12):175-178.
[144]孟昭军,孙昌志.一类永磁电动机的混沌反控制研究[J].自动化技术与应用,2006,25(008):7-9.
[145]张卓,李忠.永磁同步电动机混沌系统的反控制[J].暨南大学学报:自然科学与医学版,2001,22(003):44-46.
[146]李俊,陈基和,邹国棠.永磁直流电机的混沌反控制[J].中国电机工程学报,2006,26(8):77-81.
[147]Chacon R. Maintenance and suppression of chaos by weak harmonicperturbations: a unified view[J]. Physical Review Letters,2001,86(9):1737-1740.
[148]Chan WC, Tes CK. What form of control function can drive adiscontinuous-mode boost converter to chaos via period-doubling[J].International Journal of Circuit Theory and Applications,1998,26:281-286.
[149]Chen G. Controlling chaos and bifurcations in engineering systems[M]. CRC,2000.
[150]Chen G, Zhou J, Hsu SB. Linear superposition of chaotic and orderly vibrationson two serially connected strings with a van der Pol joint[J]. InternationalJournal of Bifurcation and Chaos in Applied Sciences and Engineering,1996,6(8):1509-1528.
[151]Chen G, Huang T, Juang J et al. Unbounded growth of total variations ofsnapshots of the1D linear wave equation due to the chaotic behavior of iteratesof composite nonlinear boundary reflection relations[J]. LECTURE NOTES INPURE AND APPLIED MATHEMATICS,2001:15-44.
[152]Chen M, Chen Z, Chen G. Approximate solutions of operator equations[M].World Scientific Pub Co Inc,1997.
[153]Lü J, Zhou T, Chen G et al. Generating chaos with a switching piecewise-linearcontroller[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science,2002,12(2):344.
[154]Lü J, Yu X, Chen G. Generating chaotic attractors with multiple merged basins ofattraction: A switching piecewise-linear control approach[J]. Circuits andSystems I: Fundamental Theory and Applications, IEEE Transactions on,2003,50(2):198-207.
[155]Wang Z, Chau KT. Anti-control of chaos of a permanent magnet DC motorsystem for vibratory compactors[J]. Chaos, Solitons&Fractals,2008,36(3):694-708.
[156]Diekmann O. Delay equations: functional-, complex-, and nonlinear analysis[M].Springer,1995.
[157]Kuang Y. Delay differential equations: with applications in populationdynamics[M]. Academic Pr,1993.
[158]Glendinning P. Stability, instability, and chaos: An introduction to the theory ofnonlinear differential equations[M]. Cambridge Univ Pr,1994.
[159]Mensour B, Longtin A. Controlling chaos to store information indelay-differential equations[J]. Physics Letters A,1995,205(1):18-24.
[160]Lu H, He Z. Chaotic behavior in first-order autonomous continuous-time systemswith delay[J]. Circuits and Systems I: Fundamental Theory and Applications,IEEE Transactions on,1996,43(8):700-702.
[161]Celka P. Delay-differential equation versus1D-map: Application to chaoscontrol[J]. Physica D: Nonlinear Phenomena,1997,104(2):127-147.
[162]陈关荣,汪小帆.动力系统的混沌化[M].上海:上海交通大学出版社,2006.
[163]任海鹏,刘丁,韩崇昭.基于直接延迟反馈的混沌反控制[J].物理学报,2006,55(6):2694-2698.
[164]Stépán G. Retarded Dynamical Systems: Stability and Characteristic Functions:proceedings of the Pitman Research Notes in Mathematics Series, New York,1989[C]. Longman Scientific and Technical, Wiley.
[165]秦元勋,刘永清,王联.带有时滞的动力系统的运动稳定性[M].科学出版社,1989.
[166]Hassard BD. Counting Roots of the Characteristic Equation for LinearDelay-Differential Systems[J]. Journal of Differential Equations,1997,136(2):222-235.
[167]Kolmanovski VB, Nosov VR. Stability of Functional Differential Equations[M].London: Academic Press,1986.
[168]Olgac N, Sipahi R. An exact method for the stability analysis of time-delayedlinear time-invariant systems[J]. IEEE Transactions on Automatic Control,2002,47:793–797.
[169]Faria T, Magalhaes LT. Normal forms for retarded functional differentialequations with parameters and applications to Hopf bifurcation[J]. Journal ofDifferential Equations,1995,122(2):181-200.
[170]Faria T, Magalhaes LT. Normal forms for retarded functional differentialequations and applications to Bogdanov-Takens singularity[J]. Journal ofDifferential Equations,1995,122(2):201-224.
[171]Stech HW. Hopf bifurcation calculations for functional differential equations[J].J MATH ANAL APPLIC,1985,109(2):471-491.
[172]Hu H, Dowell EH, Virgin LN. Resonances of a harmonically forced Duffingoscillator with time delay state feedback[J]. Nonlinear Dynamics,1998,15(4):311-327.
[173]Wang XF, Chen G, Yu X. Anticontrol of chaos in continuous-time systems viatime-delay feedback[J]. Chaos: An Interdisciplinary Journal of NonlinearScience,2000,10(4):771-779.
[174]Wang XF, Chen G. Chaotifying a stable LTI system by tiny feedback control[J].Circuits and Systems I: Fundamental Theory and Applications, IEEETransactions on,2000,47(3):410-415.
[175]Wang XF, Zhong GQ, Tang KS et al. Generating chaos in Chua's circuit viatime-delay feedback[J]. Circuits and Systems I: Fundamental Theory andApplications, IEEE Transactions on,2001,48(9):1151-1156.
[176]Wang XF, Chen GR, Man KF. Making a continuous-time minimum phase systemchaotic by time-delay feedback[J]. IEEE Transactions on Circuit and Systems,2001,48(5):641–645.
[177]Hu HY, Wang ZH. Dynamics of Controlled Mechanical Systems with DelayedFeedback[M]. Heidelberg: Springer,2002.
[178]Zhao YH. Stability of a two-dimensional airfoil with time-delayed feedbackcontrol[J]. Journal of Fluids and Structures,2009,25(1):1-25.
[179]Zhou J, Xu D, Li Y. Chaotifing Duffing-type System with Large ParameterRange Based on Optimal Time-Delay Feedback Control: proceedings of theProceedings of2010International Workshop on Chaos-Fractal Theories andApplications, Kunming, Yunnan, China, October29-31,2010[C].
[180]Heiden Uad, Walther HO. Existence of chaos in control system with delayedfeedback[J]. Journal of Differential Equations,1983,47:273-295.
[181]Tsuda Y, Tamura H, Sueoka A et al. Chaotic behaviour of a nonlinear vibratingsystem with a retarded argument[J]. JSME international journal Ser3, Vibration,control engineering, engineering for industry,1992,35(2):259-267.
[182]Chen JH. Controlling chaos and chaotification in the Chen-Lee system bymultiple time delays[J]. Chaos, Solitons&Fractals,2008,36(4):843-852.
[183]Zhao YY, Xu J. Effects of delayed feedback control on nonlinear vibrationabsorber system[J]. Journal of sound and vibration,2007,308(1-2):212-230.
[184]Li X, Ji JC, Hansen CH. Dynamics of two delay coupled van der Poloscillators[J]. Mechanics Research Communications,2006,33(5):614-627.
[185]Qian CZ, Tang JS. A time delay control for a nonlinear dynamic beam undermoving load[J]. Journal of sound and vibration,2008,309(1-2):1-8.
[186]De Paula AS, Savi MA. Controlling chaos in a nonlinear pendulum using anextended time-delayed feedback control method[J]. Chaos, Solitons&Fractals,2009,42(5):2981-2988.
[187]Cao J, Ho DWC, Yang Y. Projective synchronization of a class of delayedchaotic systems via impulsive control[J]. Physics Letters A,2009,373(35):3128-3133.
[188]Ding D, Zhu J, Luo X et al. Controlling Hopf Bifurcation in Fluid Flow Model ofInternet Congestion Control System[J]. International Journal of Bifurcation andChaos,2009,19(4):1415.
[189]Jin M, Chang PH. Simple robust technique using time delay estimation for thecontrol and synchronization of Lorenz systems[J]. Chaos, Solitons&Fractals,2009,41(5):2672-2680.
[190]Wang M, Wang X. Controlling Liu System with Different Methods[J]. ModernPhysics Letters B,2009,23(14):1805-1818.
[191]Li L, Peng H, Yang Y et al. On the chaotic synchronization of Lorenz systemswith time-varying lags[J]. Chaos, Solitons&Fractals,2009,41(2):783-794.
[192]Sen A, Mukherjee D. Chaos in the delay logistic equation with discontinuousdelays[J]. Chaos, Solitons&Fractals,2009,40(5):2126-2132.
[193]Miao Q, Tang Y, Lu S et al. Lag synchronization of a class of chaotic systemswith unknown parameters[J]. Nonlinear Dynamics,2009,57(1):107-112.
[194]Inarrea M. Chaos and its control in the pitch motion of an asymmetric magneticspacecraft in polar elliptic orbit[J]. Chaos, Solitons&Fractals,2009,40(4):1637-1652.
[195]Hu HY, Wang ZH. Singular perturbation methods for nonlinear dynamic systemswith time delays[J]. Chaos, Solitons&Fractals,2009,40(1):13-27.
[196]Xu J, Chung KW. Dynamics for a class of nonlinear systems with time delay[J].Chaos, Solitons&Fractals,2009,40(1):28-49.
[197]Chen LX, Cai GP, Pan J. Experimental study of delayed feedback control for aflexible plate[J]. Journal of sound and vibration,2009,322(4-5):629-651.
[198]Li T, Yu J, Wang Z. Delay-range-dependent synchronization criterion for Lur'esystems with delay feedback control[J]. Communications in Nonlinear Scienceand Numerical Simulation,2009,14(5):1796-1803.
[199]Vasegh N, Khaki Sedigh A. Chaos control via TDFC in time-delayed systems:The harmonic balance approach[J]. Physics Letters A,2009,373(3):354-358.
[200]Zhong H, Guo Q. Nonlinear vibration analysis of Timoshenko beams using thedifferential quadrature method[J]. Nonlinear Dynamics,2003,32(3):223-234.
[201]Howard CQ. A new cost function algorithm for adaptive-passive vibration andacoustic resonators[J]. Proceedings of Acoustics2011:2-4.
[202]Choi SB, Sohn JW, Choi SM et al. A piezostack-based active mount forbroadband frequency vibration control: experimental validation[J]. SmartMaterials and Structures,2009,18:097001.
[203]Dylejko PG, Kessissoglou NJ, Tso Y et al. Optimisation of a resonance changerto minimise the vibration transmission in marine vessels[J]. Journal of sound andvibration,2007,300(1-2):101-116.
[204]Caresta M, Kessissoglou NJ. Reduction of Hull-Radiated Noise UsingVibroacoustic Optimization of the Propulsion System[J]. Journal of ShipResearch,55(3):149-162.
[205]Howard CQ, Craig RA. Adaptive-Passive Quarter-Wave Tube Resonator Silencer:proceedings of the Proceedings of Acoustics2011: Annual conference of theAustralian Acoustical Society,2011[C].
[206]Chu SY, Soong TT, Lin CC et al. Time delay effect and compensation on directoutput feedback controlled mass damper systems[J]. Earthquake engineering&structural dynamics,2002,31(1):121-137.
[207]Fofana MS. Sufficient conditions for the stability of single and multipleregenerative chatter[J]. Chaos, Solitons&Fractals,2002,14(2):335-347.
[208]Gouskov AM, Voronov SA, Paris H et al. Nonlinear dynamics of a machiningsystem with two interdependent delays[J]. Communications in Nonlinear Scienceand Numerical Simulation,2002,7(4):207-221.
[209]Fofana MS. Delay dynamical systems and applications to nonlinear machine-toolchatter[J]. Chaos, Solitons&Fractals,2003,17(4):731-747.
[210]Zervas E. Comparative study of some experimental methods to characterize thecombustion process in a SI engine[J]. Energy,2005,30(10):1803-1816.
[211]Librescu L, Marzocca P, Silva WA. Aeroelasticity of2-D lifting surfaces withtime-delayed feedback control[J]. Journal of Fluids and Structures,2005,20(2):197-215.
[212]Li C, Liao X, Wong K. Chaotic lag synchronization of coupled time-delayedsystems and its applications in secure communication[J]. Physica D: NonlinearPhenomena,2004,194(3-4):187-202.
[213]Geng L, Osusky K, Konjeti S et al. Radiation-guided drug delivery to tumorblood vessels results in improved tumor growth delay[J]. Journal of controlledrelease,2004,99(3):369-381.
[214]Toth-Fejel SE, Pommier RF. Relationships among delay of diagnosis, extent ofdisease, and survival in patients with abdominal carcinoid tumors[J]. TheAmerican journal of surgery,2004,187(5):575-579.
[215]Routh EJ. A Treatise on the Stability of a Given State of Motion[M]. London:Macmillan1877.
[216]Hurwitz A. On the conditions under which an equation has only roots withnegative real parts[J]. Mathematicsche Annelen,1895,46:273-284.
[217]Forde J, Nelson P. Applications of Sturm sequences to bifurcation analysis ofdelay differential equation models[J]. Journal of Mathematical Analysis andApplications,2004,300(2):273-284.
[218]Wang ZH, Hu HY. Stability switches of time-delayed dynamic systems withunknown parameters[J]. Journal of sound and vibration,2000,233(2):215-233.
[219]Zhou J, Xu D, Li Y. Chaotifing duffing-type system with large parameter rangebased on optimal time-delay feedback control: proceedings of. IEEE.
[220]Nayfeh AH. Perturbation methods[M]. Wiley Online Library,1973.
[221]Kevorkian J, Cole JD. Multiple scale and singular perturbation methods[M].Springer Verlag,1996.
[222]Oueini SS, Nayfeh HA. Single-mode control of a cantilever beam under principalparametric excitation[J]. Journal of sound and vibration,1999,224(1):33-47.
[223]Wirkus S, Rand R. The dynamics of two coupled van der Pol oscillators withdelay coupling[J]. Nonlinear Dynamics,2002,30(3):205-221.
[224]Zhou J, Xu D, Li Y. An active-passive nonlinear vibration isolation method basedon optimal time-delay feedback control[J]. Journal of Vibration Engineering,2011: On press.
[225]Li YL, Xu DL, Fu YM et al. Stability and chaotification of vibration isolationfloating raft systems with time-delayed feedback control[J]. Chaos (Woodbury,NY),21(3):033115.
[226]Zhang J, Xu D, Zhou J et al. Chaotification of vibration isolation floating raftsystem via nonlinear time-delay feedback control[J]. Chaos, Solitons&Fractals,2012,45(9):1255-1265.
[227]Chen G, Wang X. Chaotification of dynamics system: theory, method andapplication[M]. Shanghai: Shanghai Jiao Tong University Press,2006.
[228]Zhou J, Xu D, Zhang J et al. Spectrum optimization-based chaotification usingtime-delay feedback control[J]. Chaos, Solitons&Fractals,2012,45:815-824.
[229]Zhou J, Xu D, Li Y. An active-passive nonlinear vibration isolation method basedon optimal time-delay feedback control[J]. Journal of Vibration Engineering,2011,24(6):639-645.