磁悬浮浮筏主动隔振系统动力学理论模型研究
|
摘要
振动控制技术是振动工程领域的一个重要分支,其主要任务就是通过一些手段使受控对象的振动水平满足人们预定的要求。舰船的减振降噪问题很久以前就引起了人们的重视,其中振动隔离技术是舰船减振降噪问题中研究最多的一项振动控制技术。隔振又可分为被动隔振和主动隔振。被动隔振是在振源与隔振对象之间加入弹性和阻尼元件,以耗散振动能量而达到隔振的目的。由于它不需外界能源,结构简单,易于实现,经济性与可靠性高,已广泛地应用在多种工程领域中。但被动隔振存在低频隔振效果不理想等固有缺点,随着科学技术的发展,被动隔振在很多方面已经很难满足人们的要求。为了达到更好的隔振效果,人们对主动隔振技术开展了深入的研究。
磁悬浮隔振技术是最近几年发展起来的一种振动主动控制技术,磁悬浮隔振系统的刚度与阻尼取决于系统的结构参数、平衡位置和控制系统,而且还可以根据需要在稳定范围内实时改变。磁悬浮隔振系统的主要元件就是磁悬浮主动隔振器,其核心技术是磁悬浮支承技术。磁悬浮支承技术是一种典型的高性能机电一体化技术,具有无接触、无摩擦、精度高、功耗低、噪声小、洁净高等优点。磁悬浮隔振器的刚度和阻尼可以根据控制参数的变化而实时改变,这为改善浮筏系统的隔振性能提供了很好的技术基础。因此,磁悬浮主动隔振技术将是振动主动控制的一个重要发展方向。
本文将磁悬浮支承技术应用于浮筏隔振系统,设计了一种磁悬浮主动隔振器,将磁悬浮主动隔振器和传统被动隔振器相结合,组成一个半主动式磁悬浮浮筏隔振系统。系统利用磁悬浮主动隔振器刚度和阻尼可控可调的特点,对宽频域的振动能起到很好的抑制作用。文中从振动控制与隔振理论分析入手,在研究浮筏隔振系统动力学模型和磁悬浮主动隔振器力学模型的基础上,采用动态子结构综合法建立了磁悬浮浮筏主动隔振系统的动力学模型。为研究磁悬浮浮筏隔振系统的隔振性能奠定了基础。
Vibration control technology is an important branch of vibration engineering field, its main task is making the vibration level of controlled objects to meet people's scheduled standard by some means. Noise and vibration reduction problem of ships caused people's attention long ago. And people have done much research on vibration isolation technology. Vibration isolation can be divided into passive vibration isolation and active vibration isolation. Passive vibration isolation which is adding elastic and damping elements between the source and isolation target, and the elastic and damping elements dissipate vibration energy to achieve the purpose of vibration isolation. Because it does not need external energy, has simple structure, easy to realize, economy and has high reliability, passive vibration isolation has been widely used in various fields in engineering. But passive vibration isolation has inherent defect such as in low frequency vibration isolation effect is undesirability. With the development of science and technology, passive vibration isolation has been difficult to meet people's requirement in many aspects. In order to achieve better vibration isolation effect, people begin to do deep research on active vibration isolation technology.
Maglev vibration isolation technology is an active vibration control technology which is developed in recent years, the stiffness and damping of maglev vibration isolation system depends on the structure parameters and equilibrium position of the system and control system, and they also can change in stable range in real-time according to need. The maglev vibration isolator is the main components of maglev vibration isolation system, and its core technology is maglev supporting technology. Maglev supporting technology is a typical kind of high-performance mechatronics technology, and it has no contact, no friction, high precision, low power consumption, and low noise, high clean and so on. The stiffness and damping of maglev vibration isolator can change in real-time according to control parameters; this provides a good technology foundation for improving the vibration isolation performance of raft vibration isolation system. Therefore the maglev active vibration isolation technology will be an important developing direction of active vibration control field.
This paper applies maglev supporting technology to the vibration isolation field, designs an active vibration isolation component which is the maglev vibration isolator, and combines the maglev active vibration isolation component and the traditional passive vibration isolation components together to make an active vibration isolation system which is maglev floating raft vibration isolation system. The system uses the controllable and adjustable characteristics of stiffness and damping of maglev active vibration isolator to restrain the vibration in a wide frequency region. This paper does research begin with analyzing the theory of vibration control and vibration isolation, and then analysis the dynamics model of the floating raft vibration isolation system and maglev active vibration isolator, on the basis of this, the dynamics model of maglev floating raft vibration isolation system is deduced by dynamic substructure method. This laid a foundation for studying vibration isolation performance of maglev floating raft vibration isolation system.
磁悬浮隔振技术是最近几年发展起来的一种振动主动控制技术,磁悬浮隔振系统的刚度与阻尼取决于系统的结构参数、平衡位置和控制系统,而且还可以根据需要在稳定范围内实时改变。磁悬浮隔振系统的主要元件就是磁悬浮主动隔振器,其核心技术是磁悬浮支承技术。磁悬浮支承技术是一种典型的高性能机电一体化技术,具有无接触、无摩擦、精度高、功耗低、噪声小、洁净高等优点。磁悬浮隔振器的刚度和阻尼可以根据控制参数的变化而实时改变,这为改善浮筏系统的隔振性能提供了很好的技术基础。因此,磁悬浮主动隔振技术将是振动主动控制的一个重要发展方向。
本文将磁悬浮支承技术应用于浮筏隔振系统,设计了一种磁悬浮主动隔振器,将磁悬浮主动隔振器和传统被动隔振器相结合,组成一个半主动式磁悬浮浮筏隔振系统。系统利用磁悬浮主动隔振器刚度和阻尼可控可调的特点,对宽频域的振动能起到很好的抑制作用。文中从振动控制与隔振理论分析入手,在研究浮筏隔振系统动力学模型和磁悬浮主动隔振器力学模型的基础上,采用动态子结构综合法建立了磁悬浮浮筏主动隔振系统的动力学模型。为研究磁悬浮浮筏隔振系统的隔振性能奠定了基础。
Vibration control technology is an important branch of vibration engineering field, its main task is making the vibration level of controlled objects to meet people's scheduled standard by some means. Noise and vibration reduction problem of ships caused people's attention long ago. And people have done much research on vibration isolation technology. Vibration isolation can be divided into passive vibration isolation and active vibration isolation. Passive vibration isolation which is adding elastic and damping elements between the source and isolation target, and the elastic and damping elements dissipate vibration energy to achieve the purpose of vibration isolation. Because it does not need external energy, has simple structure, easy to realize, economy and has high reliability, passive vibration isolation has been widely used in various fields in engineering. But passive vibration isolation has inherent defect such as in low frequency vibration isolation effect is undesirability. With the development of science and technology, passive vibration isolation has been difficult to meet people's requirement in many aspects. In order to achieve better vibration isolation effect, people begin to do deep research on active vibration isolation technology.
Maglev vibration isolation technology is an active vibration control technology which is developed in recent years, the stiffness and damping of maglev vibration isolation system depends on the structure parameters and equilibrium position of the system and control system, and they also can change in stable range in real-time according to need. The maglev vibration isolator is the main components of maglev vibration isolation system, and its core technology is maglev supporting technology. Maglev supporting technology is a typical kind of high-performance mechatronics technology, and it has no contact, no friction, high precision, low power consumption, and low noise, high clean and so on. The stiffness and damping of maglev vibration isolator can change in real-time according to control parameters; this provides a good technology foundation for improving the vibration isolation performance of raft vibration isolation system. Therefore the maglev active vibration isolation technology will be an important developing direction of active vibration control field.
This paper applies maglev supporting technology to the vibration isolation field, designs an active vibration isolation component which is the maglev vibration isolator, and combines the maglev active vibration isolation component and the traditional passive vibration isolation components together to make an active vibration isolation system which is maglev floating raft vibration isolation system. The system uses the controllable and adjustable characteristics of stiffness and damping of maglev active vibration isolator to restrain the vibration in a wide frequency region. This paper does research begin with analyzing the theory of vibration control and vibration isolation, and then analysis the dynamics model of the floating raft vibration isolation system and maglev active vibration isolator, on the basis of this, the dynamics model of maglev floating raft vibration isolation system is deduced by dynamic substructure method. This laid a foundation for studying vibration isolation performance of maglev floating raft vibration isolation system.
引文
[1]郝刚.舰船减振浮筏动力特性研究[D].大连：大连理工大学,2002
[2]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(2)：5-8
[3]杜冬.动力吸振器控制算法研究及在舰船设备减振中的应用[D].上海：上海交通大学,2007
[4]胡业发,周祖德,江征风.磁力轴承的基础理论与应用[M].北京：机械工业出版社,2006：1～3
[5]吴伟光,马履中,朱伟,等.新型混合磁悬浮主动隔振的研究*[J].机械设计,2008,25(5)：49～51
[6]赵良省.噪声与振动控制技术[M].北京：化学工业出版社,2004：37-47
[7]吴祥明.磁悬浮列车[M].上海：上海科学技术出版社,2003：12～20
[8]曹贻鹏.船舶柴油发电机组隔振与隔声设计[D].哈尔滨：哈尔滨工程大学,2005
[9]刘保国.、复杂隔振系统振动传递特性及实验研究[D].济南：山东大学,2007
[10]沈密群,严济宽.舰船浮筏装置工程实例[J].噪声与振动控制,1994(5)：21～23
[11]张华良,傅志方,瞿祖清.浮筏隔振系统各主要参数对系统隔振性能的影响[J].振动与冲击,2000(19)：5-8
[12]俞微,张建武,沈荣瀛,等.浮筏隔振系统功率流的实验研究[J].振动、测试与诊断,1996,16(2)：44～48
[13]张国良.浮筏技术在舰艇抑振降噪中的应用[J].舰船工程研究,1994(4)：16～19
[14]熊冶平,宋孔杰,韩玉长.复杂柔性藕合系统的功率流传递谱[J].声学学报,1996,21(4)：368～374
[15]宋孔杰,张蔚波,牛军川.功率流理论在柔性振动控制技术中的应用与发展[J].机械工程学报,2003,39(9)：23～28
[16]Junchuan Niu, Kongjie Song, C.W. Lim. On active vibration isolation of floating raft system[J]. Journal of Sound and Vibration,2005(285):391～406
[17]巫影.浮伐减振降噪理论研究与仿真[D].武汉：武汉理工大学,2002
[18]马永涛,周炎.舰船浮筏隔振技术综述[J].舰船科学技术,2008,30(4)：22～26
[19]尚国清,李巍.关于舰船浮筏系统的特征演化[J].舰船科学技术,1999(1)：21～23
[20]Z. Jason Geng, Leonard S. Haynes. Six Degree-of-Freedom Active Vibration Control Using the Stewart Platforms[J]. IEEE transactions on control systems technology,1994,2(1): 45-53
[21]S.O. Reza Moheimani, Ian R. Petersen, Himanshu R. Pota. Emerging technologies for active noise and vibration control systems[J]. Control Engineering Practice,2004(12):987～988
[22]D. A. Howe, A. Hati, C. Nelson et al. Active vibration-induced PM noise control in optical fibers preliminary studies[J]. National Institute of Standards& Technology (NIST), Boulder, CO, USA.553～556
[23]尚国清,郭有松.舰船振动隔离技术理论与应用研究进展[J].舰船科学技术,2006,28(1)：43～47
[24]吴崇健,杜堃,张京伟,等.浮筏隔振系统的设计方法[J].舰船工程研究(季刊),1996(3)：37～45
[25]尚国清,林立.浮筏装置系统的动力学特性分析[J].舰船科学技术,2006(6)：11-15
[26]林立,胡剑凌.减振浮筏振动响应研究[J].噪声与振动控制,1996(5)：2-6
[27]刘永明,沈荣赢,严济宽.多层隔振系统冲击响应研究[J].噪声与振动控制,1996(3)：2-8
[28]吴广明,沈荣赢,李俊,等.多层隔振系统的动力学模型[J].振动与冲击,2005,24(2)：16～20
[29]Timothy N. Chang, Bhaskar Dani, Zhiming Ji et al. Contactless magnetic transmission system Vibration control and resonance compensation[J]. IEEE/Asme transactions on mechatronics,2004,9(2):458～461
[30]杜奎,伍先俊,程广利,等.浮筏隔振系统隔振器最佳布置方案研究[J].海军工程大学学报,2005,17(2)：92～94
[31]王永远.船舶动力系统隔振技术研究[D].武汉：武汉理工大学,2008
[32]张鲲,孙红灵,陈海波,等.带有动力吸振器的浮筏隔振系统的功率流传递特性分析[J].中国科学技术大学学报,2007,37(1)：13～19
[33]P.Gardonio,S.J.Elliott, R. J.Pinnington. Active isolation of structural vibration on a multiple degree of freedom system,Part Ⅰ:the dynamics of the system[J]. Journal of Sound and Vibration,1997,207(1):61～93
[34]P.Gardonio,S.J.Elliott, R. J.Pinnington. Active isolation of structural vibration on a multiple degree of freedom system,Part II effectiveness of active control strategies[J]. Journal of Sound and Vibration,1997,207(1):95～121
[35]Takeshi Mizuno, Masaya Takasaki, Daisuke Kishita et al. Vibration isolation system combining zero-power magnetic suspension with springs[J]. Control Engineering Practice, 2007(15):187～196
[36]Md. Emdadul Hoque, Masaya Takasaki, Yuji Ishino et al. Development of a three-axis active vibration isolator using zero-power Control[J]. IEEE/ASME TRANSACTIONS ON MECHATRONICS,2006,11(4):462～469
[37]Hironori HOSHINO, Erimitsu SUZUKI, Ken WATANABE, ph.D.Reduction of vibrations in maglev vehicles using active primary and secondary suspension control[J] dh. QR of RTRI, 2008,49(2):113～118
[38]王福强,马履中,沈春根.磁悬浮式隔振技术的特性分析与研究[J].机械设计与研究,2003,19(1)：44～45
[39]赵冉,王永.基于自适应滑模控制的主动磁悬浮隔振系统[J].自动化与仪表,2008(10)：4-8
[40]周文.磁悬浮浮筏隔振系统传递特性的研究[D].武汉：武汉理工大学,2009
[41]王福强.三平移磁悬浮式隔振器的设计与应用研究[D].镇江：江苏大学,2003
[42]吴伟光,马履中.永磁电磁混合悬浮隔振主动控制装置[J].农业机械学报,2007,38(7)：183～185
[43]王福强,马履中,沈春根.磁悬浮式隔振技术的特性分析与研究[J].机械设计与研究,2003,19(1)：44～46
[44]尚国清,邱伯华.关于浮筏系统的动力学建模分析[J].舰船科学技术,1999(4)：24～28
[45]祝华.浮筏装置的理论建模与分析方法[J].舰船科学技术,1994(2)：14～19
[46]Y. Liu, T.P. Waters, M.J. Brennan. A comparison of semi-active damping control strategies for vibration isolation of harmonic disturbances [J]. Journal of Sound and Vibration, 2005(280):21-39
[47]Y. Zhang, A.G. Alleyne, D. Zheng. A hybrid control strategy for active vibration isolation with electrohydraulic actuators [J]. Control Engineering Practice,2005(13):279～289
[48]L. Benassi, S.J. Elliott, P. Gardonio. Active vibration isolation using an inertial actuator with local force feedback control [J]. Journal of Sound and Vibration,2004(276):157～179
[49]David L. Trumper, Ming-chih Weng, Robert J. Ritter. Magnetic Suspension and Vibration Control of Beams for Non-contact Processing [J]. International Conference on Control Applications. Hawai'i:IEEE,1999:551～557
[50]余林波,黄其柏,张永波,等.双层浮筏隔振系统筏体结构与隔振特性的研究[J].噪声与振动控制,2007(4)：7-9
[51]崔艳.复杂隔振系统的频率平均功率流分析与效果评估研究[D].济南：山东大学,2007
[52]蒋金夏,刘永明.立体浮筏隔振系统的模态机械阻抗综合法研究[J].噪声与振动控制,2006(4)：20～23
[53]王孚懋,杨龙,赵丽芳,等.水泵机组浮筏隔振系统研究[J].噪声与振动控制,2008(5)：36～39
[54]黄其柏.工程噪声控制学[M].武汉：华中理工大学出版社,1999：4-8
[55]朱石坚,楼京俊,何其伟,等编著.振动理论与隔离技术[M].北京：国防工业出版社,2006：212～213,269～283
[56]严济宽著.机械振动隔离技术[M].北京：上海科学技术出版社,1985：1～11
[57]李德葆,张元润编著.振动测量与实验分析[M].北京：机械工业出版社,1991：343～344
[58]徐洋,华宏星,张志谊.舰船主动隔振技术综述[J].舰船科学技术,2008,30(2)：27～29
[59]李维嘉,曹青松.传播振动主动控制的研究进展和评述[J].中国造船,2007,48(2)：68～70
[60]EMDADUL H, MASAYA T, YUJI I. Development of a three-axis active vibration isolator using zero-power control [J]. IEEE/ASME TRANSACTIONS ON MECHATRONICS,2006, 8(11):462～469
[61]T.-J. Yeh, Ying-Jer Chung, Wei-Chung Wu. Sliding Control of Magnetic Bearing Systems [J]. Journal of Dynamic Systems, Measurement and Control,2001,123:353～356
[62]宋春生,周祖德,胡业发.变刚度浮筏隔振系统功率流传递特性分析[J].武汉理工大学学报,2009,31(3)：417～424
[63]Ha-YongKin, Seung-JongKin. An Effective Way to Combine Radial and Axial Magnetic Bearings in a Unit [C]. Proc 10th Int Symp on Magnetic Bearings, Martigny, Switzerland, Aug 21～23,2006
[2]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(2)：5-8
[3]杜冬.动力吸振器控制算法研究及在舰船设备减振中的应用[D].上海：上海交通大学,2007
[4]胡业发,周祖德,江征风.磁力轴承的基础理论与应用[M].北京：机械工业出版社,2006：1～3
[5]吴伟光,马履中,朱伟,等.新型混合磁悬浮主动隔振的研究*[J].机械设计,2008,25(5)：49～51
[6]赵良省.噪声与振动控制技术[M].北京：化学工业出版社,2004：37-47
[7]吴祥明.磁悬浮列车[M].上海：上海科学技术出版社,2003：12～20
[8]曹贻鹏.船舶柴油发电机组隔振与隔声设计[D].哈尔滨：哈尔滨工程大学,2005
[9]刘保国.、复杂隔振系统振动传递特性及实验研究[D].济南：山东大学,2007
[10]沈密群,严济宽.舰船浮筏装置工程实例[J].噪声与振动控制,1994(5)：21～23
[11]张华良,傅志方,瞿祖清.浮筏隔振系统各主要参数对系统隔振性能的影响[J].振动与冲击,2000(19)：5-8
[12]俞微,张建武,沈荣瀛,等.浮筏隔振系统功率流的实验研究[J].振动、测试与诊断,1996,16(2)：44～48
[13]张国良.浮筏技术在舰艇抑振降噪中的应用[J].舰船工程研究,1994(4)：16～19
[14]熊冶平,宋孔杰,韩玉长.复杂柔性藕合系统的功率流传递谱[J].声学学报,1996,21(4)：368～374
[15]宋孔杰,张蔚波,牛军川.功率流理论在柔性振动控制技术中的应用与发展[J].机械工程学报,2003,39(9)：23～28
[16]Junchuan Niu, Kongjie Song, C.W. Lim. On active vibration isolation of floating raft system[J]. Journal of Sound and Vibration,2005(285):391～406
[17]巫影.浮伐减振降噪理论研究与仿真[D].武汉：武汉理工大学,2002
[18]马永涛,周炎.舰船浮筏隔振技术综述[J].舰船科学技术,2008,30(4)：22～26
[19]尚国清,李巍.关于舰船浮筏系统的特征演化[J].舰船科学技术,1999(1)：21～23
[20]Z. Jason Geng, Leonard S. Haynes. Six Degree-of-Freedom Active Vibration Control Using the Stewart Platforms[J]. IEEE transactions on control systems technology,1994,2(1): 45-53
[21]S.O. Reza Moheimani, Ian R. Petersen, Himanshu R. Pota. Emerging technologies for active noise and vibration control systems[J]. Control Engineering Practice,2004(12):987～988
[22]D. A. Howe, A. Hati, C. Nelson et al. Active vibration-induced PM noise control in optical fibers preliminary studies[J]. National Institute of Standards& Technology (NIST), Boulder, CO, USA.553～556
[23]尚国清,郭有松.舰船振动隔离技术理论与应用研究进展[J].舰船科学技术,2006,28(1)：43～47
[24]吴崇健,杜堃,张京伟,等.浮筏隔振系统的设计方法[J].舰船工程研究(季刊),1996(3)：37～45
[25]尚国清,林立.浮筏装置系统的动力学特性分析[J].舰船科学技术,2006(6)：11-15
[26]林立,胡剑凌.减振浮筏振动响应研究[J].噪声与振动控制,1996(5)：2-6
[27]刘永明,沈荣赢,严济宽.多层隔振系统冲击响应研究[J].噪声与振动控制,1996(3)：2-8
[28]吴广明,沈荣赢,李俊,等.多层隔振系统的动力学模型[J].振动与冲击,2005,24(2)：16～20
[29]Timothy N. Chang, Bhaskar Dani, Zhiming Ji et al. Contactless magnetic transmission system Vibration control and resonance compensation[J]. IEEE/Asme transactions on mechatronics,2004,9(2):458～461
[30]杜奎,伍先俊,程广利,等.浮筏隔振系统隔振器最佳布置方案研究[J].海军工程大学学报,2005,17(2)：92～94
[31]王永远.船舶动力系统隔振技术研究[D].武汉：武汉理工大学,2008
[32]张鲲,孙红灵,陈海波,等.带有动力吸振器的浮筏隔振系统的功率流传递特性分析[J].中国科学技术大学学报,2007,37(1)：13～19
[33]P.Gardonio,S.J.Elliott, R. J.Pinnington. Active isolation of structural vibration on a multiple degree of freedom system,Part Ⅰ:the dynamics of the system[J]. Journal of Sound and Vibration,1997,207(1):61～93
[34]P.Gardonio,S.J.Elliott, R. J.Pinnington. Active isolation of structural vibration on a multiple degree of freedom system,Part II effectiveness of active control strategies[J]. Journal of Sound and Vibration,1997,207(1):95～121
[35]Takeshi Mizuno, Masaya Takasaki, Daisuke Kishita et al. Vibration isolation system combining zero-power magnetic suspension with springs[J]. Control Engineering Practice, 2007(15):187～196
[36]Md. Emdadul Hoque, Masaya Takasaki, Yuji Ishino et al. Development of a three-axis active vibration isolator using zero-power Control[J]. IEEE/ASME TRANSACTIONS ON MECHATRONICS,2006,11(4):462～469
[37]Hironori HOSHINO, Erimitsu SUZUKI, Ken WATANABE, ph.D.Reduction of vibrations in maglev vehicles using active primary and secondary suspension control[J] dh. QR of RTRI, 2008,49(2):113～118
[38]王福强,马履中,沈春根.磁悬浮式隔振技术的特性分析与研究[J].机械设计与研究,2003,19(1)：44～45
[39]赵冉,王永.基于自适应滑模控制的主动磁悬浮隔振系统[J].自动化与仪表,2008(10)：4-8
[40]周文.磁悬浮浮筏隔振系统传递特性的研究[D].武汉：武汉理工大学,2009
[41]王福强.三平移磁悬浮式隔振器的设计与应用研究[D].镇江：江苏大学,2003
[42]吴伟光,马履中.永磁电磁混合悬浮隔振主动控制装置[J].农业机械学报,2007,38(7)：183～185
[43]王福强,马履中,沈春根.磁悬浮式隔振技术的特性分析与研究[J].机械设计与研究,2003,19(1)：44～46
[44]尚国清,邱伯华.关于浮筏系统的动力学建模分析[J].舰船科学技术,1999(4)：24～28
[45]祝华.浮筏装置的理论建模与分析方法[J].舰船科学技术,1994(2)：14～19
[46]Y. Liu, T.P. Waters, M.J. Brennan. A comparison of semi-active damping control strategies for vibration isolation of harmonic disturbances [J]. Journal of Sound and Vibration, 2005(280):21-39
[47]Y. Zhang, A.G. Alleyne, D. Zheng. A hybrid control strategy for active vibration isolation with electrohydraulic actuators [J]. Control Engineering Practice,2005(13):279～289
[48]L. Benassi, S.J. Elliott, P. Gardonio. Active vibration isolation using an inertial actuator with local force feedback control [J]. Journal of Sound and Vibration,2004(276):157～179
[49]David L. Trumper, Ming-chih Weng, Robert J. Ritter. Magnetic Suspension and Vibration Control of Beams for Non-contact Processing [J]. International Conference on Control Applications. Hawai'i:IEEE,1999:551～557
[50]余林波,黄其柏,张永波,等.双层浮筏隔振系统筏体结构与隔振特性的研究[J].噪声与振动控制,2007(4)：7-9
[51]崔艳.复杂隔振系统的频率平均功率流分析与效果评估研究[D].济南：山东大学,2007
[52]蒋金夏,刘永明.立体浮筏隔振系统的模态机械阻抗综合法研究[J].噪声与振动控制,2006(4)：20～23
[53]王孚懋,杨龙,赵丽芳,等.水泵机组浮筏隔振系统研究[J].噪声与振动控制,2008(5)：36～39
[54]黄其柏.工程噪声控制学[M].武汉：华中理工大学出版社,1999：4-8
[55]朱石坚,楼京俊,何其伟,等编著.振动理论与隔离技术[M].北京：国防工业出版社,2006：212～213,269～283
[56]严济宽著.机械振动隔离技术[M].北京：上海科学技术出版社,1985：1～11
[57]李德葆,张元润编著.振动测量与实验分析[M].北京：机械工业出版社,1991：343～344
[58]徐洋,华宏星,张志谊.舰船主动隔振技术综述[J].舰船科学技术,2008,30(2)：27～29
[59]李维嘉,曹青松.传播振动主动控制的研究进展和评述[J].中国造船,2007,48(2)：68～70
[60]EMDADUL H, MASAYA T, YUJI I. Development of a three-axis active vibration isolator using zero-power control [J]. IEEE/ASME TRANSACTIONS ON MECHATRONICS,2006, 8(11):462～469
[61]T.-J. Yeh, Ying-Jer Chung, Wei-Chung Wu. Sliding Control of Magnetic Bearing Systems [J]. Journal of Dynamic Systems, Measurement and Control,2001,123:353～356
[62]宋春生,周祖德,胡业发.变刚度浮筏隔振系统功率流传递特性分析[J].武汉理工大学学报,2009,31(3)：417～424
[63]Ha-YongKin, Seung-JongKin. An Effective Way to Combine Radial and Axial Magnetic Bearings in a Unit [C]. Proc 10th Int Symp on Magnetic Bearings, Martigny, Switzerland, Aug 21～23,2006