含负刚度器件的Maxwell模型动力吸振器的参数优化
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摘要
将黏弹性材料模型中的Maxwell模型引入到吸振系统。形成一种含负刚度器件的Maxwell模型动力吸振器,并对该模型的参数进行优化。建立系统的运动微分方程,得到系统的解析解;利用固定点理论将系统的三个固定点调整到同一高度,求出系统的最优频率比和最优负刚度比,并根据H_∞优化准则得到系统的最优阻尼比;分别在简谐激励和随机激励条件下,与几种经典动力吸振器模型对比证明了含负刚度的Maxwell模型动力吸振器有较好的吸振效果。
The maxwell model of the viscoelastic material was applied to a dynamic vibration absorber(DVA) system to form a Maxwell model dynamic vibration absorber with negative stiffness spring, and the parameters of the model were optimized. At first, the analytical system solution was obtained based on the established motion differential equation. Then, three fixed points were found in the amplitude-frequency curves of the primary system. The design formulae for the optimal tuning ratio of the DVA were obtained by adjusting the three fixed points to the same height according to the fixed-point theory. According to the characteristics of negative stiffness elements, the optimal negative stiffness ratio was obtained and it could keep the system stable. The optimal damping ratio was obtained by minimizing the maximum value of the amplitude frequency curves. At last, the comparisons of the presented DVA with three other traditional DVAs under the harmonic and random excitations show that the presented DVA in this paper performs better in vibration absorption.
The maxwell model of the viscoelastic material was applied to a dynamic vibration absorber(DVA) system to form a Maxwell model dynamic vibration absorber with negative stiffness spring, and the parameters of the model were optimized. At first, the analytical system solution was obtained based on the established motion differential equation. Then, three fixed points were found in the amplitude-frequency curves of the primary system. The design formulae for the optimal tuning ratio of the DVA were obtained by adjusting the three fixed points to the same height according to the fixed-point theory. According to the characteristics of negative stiffness elements, the optimal negative stiffness ratio was obtained and it could keep the system stable. The optimal damping ratio was obtained by minimizing the maximum value of the amplitude frequency curves. At last, the comparisons of the presented DVA with three other traditional DVAs under the harmonic and random excitations show that the presented DVA in this paper performs better in vibration absorption.
引文
[1]刘耀宗,郁殿龙,赵宏刚,等.被动式动力吸振技术研究进展[J].机械工程学报,2007,43(3):14-21.LIU Yaozong,YU Dianlong,ZHAO Honggang,et al. Review of passive dynamic vibration absorbers[J]. Chinese Journal of Mechanical Engineering,2007,43(3):14-21.
[2]帅词俊,段吉安,王炯.关于黏弹性材料的广义Maxwell模型[J].力学学报,2006,38(4):565-569.SHUAI Cijun,DUAN Ji’an,WANG Jiong. A method of establishing generalized maxwell model for viscoelastic material[J]. Chinese Journal of Theoretical and Applied Mechanics,2006,38(4):565-569.
[3]张小兵,尹韶辉,朱科军,等.基于广义Maxwell模型的非球面光学镜片成型模拟[J].材料导报,2013,27(20):148-152.ZHANG Xiaobing, YIN Shaohui, SONG Kejun, et al.Simulation of compression molding aspherical glass lenses based on generalized maxwell madel[J]. Meterials Review,2013,27(20):148-152.
[4]王观石,胡世丽,李志文,等.完整岩体对测井频率应力波的滤波特性[J].振动与冲击,2014,33(23):127-132.WANG Guanshi, HU Shili, LI Zhiwen, et al. Filtering property of intact rock mass to stress wave within scope of log frequency[J]. Journal of Vibration and Shock,2014,33(23):127-132.
[5]周圆兀,王囡囡.设置黏滞阻尼器结构的耗能减震分析[J].广西科技大学学报,2015(2):14-19.ZHOU Yuanwu,WANG Nannan. Seismic mitigation analysis of adding viscous damper structure[J]. Journal of Guangxi University of Science and Technology,2015(2):14-19.
[6]盛美萍,王敏庆,孙进才.噪声与振动控制技术基础[M].北京:科学出版社,2007.
[7] FRAHM H. Device for damping vibrations of bodies:USP99525435A[P]. 1909-10-30.
[8]ORMONDROYD J,DEN HARTOG J P. The theory of the dynamic vibration absorber[J]. Journal of Applied Mechanics,1928,50:9-22.
[9]HAHNKAMM E. The damping of the foundation vibrations at varying excitation frequency[J]. Master of Architecture,1932,4:192-201.
[10]BROCK J E. A note on the damped vibration absorber[J].Journal of Applied Mechanics,1946,13:A284.
[11]NISHIHARA O,ASAMI T. Close-form solutions to the exact optimizations of dynamic vibration absorber(minimizations of the maximum amplitude magnification factors)[J]. Journal of Vibration and Acoustics,2002,124:576-582.
[12]ASAMI T,NISHIHARA O,BAZ A M. Analytical solutions to H∞and H2 optimization of dynamic vibration absorbers attached to damped linear systems[J]. Journal of Vibration and Acoustics,2002,124:284-295.
[13]REN M Z. A variant design of the dynamic vibration absorber[J]. Journal of Sound and Vibration,2001,245(4):762-770.
[14]LIU K F,LIU J. The damped dynamic vibration absorbers:revisited and new result[J]. Journal of Sound and Vibration,2005,284(3):1181-1189.
[15] ASAMI T,NISHIHARA O. Analytical and experimental evaluation of an air damped dynamic vibration absorber:design optimizations of the three-element type model[J].Journal of Vibration and Acoustics,1999,121:334-342.
[16] ASAMI T,NISHIHARA O. H2 optimization of the threeelement type dynamic vibration absorbers[J]. Journal of Vibration and Acoustics,2002,124:583-592.
[17] SHEN Y J, WANG L, YANG S P, et al. Nonlinear dynamical analysis and parameters optimization of four semiactive on-off dynamic vibration absorbers[J]. Journal of Vibration and Control,2013,19(1):143-160.
[18]SHEN Y J,AHMADIAN M. Nonlinear dynamical analysis on four semi-active dynamic vibration absorbers with time delay[J]. Shock and Vibration,2013,20(4):649-663.
[19] ALABUZHEV P M,RIVIN E I. Vibration protecting and measuring systems with quasi-zero stiffness[M]. New York:Hemisphere Pub. Corp,1989.
[20]PLATUS D L. Negative-stiffness-mechanism vibration isolation systems[J]. In:International Society for Optics and Photonics,1992,1619:44-54.
[21]彭献,陈树年.负刚度的工作原理及应用初探[J].湖南大学学报(自然科学版),1992,19(4):89-94.PENG Xian,CHEN Shunian. Research on theory of negative stiffness and its application[J]. Journal of Hunan University(Natural Seiences),1992,19(4):89-94.
[22]彭解华,陈树年.正负刚度并联结构的稳定性及应用研究[J].振动、测试与诊断,1995,15(2):14-18.PENG Jiehua,CHEN Shunian. The stability and application of a structure with positive stiffness element and negative stiffness element[J]. Journal of Vibration,Measurement&Diagnosis,1995,15(2):14-18.
[23] ACAR M A,YILMAZ C. Design of an adaptive-passive dynamic vibration absorber composed of a string-mass system equipped with negative stiffness tension adjusting mechanism[J]. Journal of Sound and Vibration,2013,332(2):231-245.
[24]彭海波,申永军,杨绍普.一种含负刚度元件的新型动力吸振器的参数优化[J].力学学报,2015,47(2):320-327.PENG Haibo,SHEN Yongjun,YANG Shaopu. Parameters optimization of a new type of dynamic vibration absorber with negative stiffness[J]. Chinese Journal of Theoretical and Applied Mechanics,2015,47(2):320-327.
[25]SHEN Y J,WANG X R,YANG S P,et al. Parameters optimization for a kind of dynamic vibration absorber with negative stiffness[J]. Mathematical Problems in Engineering,2016(4):1-10.
[26] ANTONIADIS I,CHRONOPOULOS D,SPITAS V,et al.Hyper-damping properties of a stiff and stable linear oscillator with a negative stiffness element[J]. Journal of Sound and Vibration,2015,346(1):37-52.
[2]帅词俊,段吉安,王炯.关于黏弹性材料的广义Maxwell模型[J].力学学报,2006,38(4):565-569.SHUAI Cijun,DUAN Ji’an,WANG Jiong. A method of establishing generalized maxwell model for viscoelastic material[J]. Chinese Journal of Theoretical and Applied Mechanics,2006,38(4):565-569.
[3]张小兵,尹韶辉,朱科军,等.基于广义Maxwell模型的非球面光学镜片成型模拟[J].材料导报,2013,27(20):148-152.ZHANG Xiaobing, YIN Shaohui, SONG Kejun, et al.Simulation of compression molding aspherical glass lenses based on generalized maxwell madel[J]. Meterials Review,2013,27(20):148-152.
[4]王观石,胡世丽,李志文,等.完整岩体对测井频率应力波的滤波特性[J].振动与冲击,2014,33(23):127-132.WANG Guanshi, HU Shili, LI Zhiwen, et al. Filtering property of intact rock mass to stress wave within scope of log frequency[J]. Journal of Vibration and Shock,2014,33(23):127-132.
[5]周圆兀,王囡囡.设置黏滞阻尼器结构的耗能减震分析[J].广西科技大学学报,2015(2):14-19.ZHOU Yuanwu,WANG Nannan. Seismic mitigation analysis of adding viscous damper structure[J]. Journal of Guangxi University of Science and Technology,2015(2):14-19.
[6]盛美萍,王敏庆,孙进才.噪声与振动控制技术基础[M].北京:科学出版社,2007.
[7] FRAHM H. Device for damping vibrations of bodies:USP99525435A[P]. 1909-10-30.
[8]ORMONDROYD J,DEN HARTOG J P. The theory of the dynamic vibration absorber[J]. Journal of Applied Mechanics,1928,50:9-22.
[9]HAHNKAMM E. The damping of the foundation vibrations at varying excitation frequency[J]. Master of Architecture,1932,4:192-201.
[10]BROCK J E. A note on the damped vibration absorber[J].Journal of Applied Mechanics,1946,13:A284.
[11]NISHIHARA O,ASAMI T. Close-form solutions to the exact optimizations of dynamic vibration absorber(minimizations of the maximum amplitude magnification factors)[J]. Journal of Vibration and Acoustics,2002,124:576-582.
[12]ASAMI T,NISHIHARA O,BAZ A M. Analytical solutions to H∞and H2 optimization of dynamic vibration absorbers attached to damped linear systems[J]. Journal of Vibration and Acoustics,2002,124:284-295.
[13]REN M Z. A variant design of the dynamic vibration absorber[J]. Journal of Sound and Vibration,2001,245(4):762-770.
[14]LIU K F,LIU J. The damped dynamic vibration absorbers:revisited and new result[J]. Journal of Sound and Vibration,2005,284(3):1181-1189.
[15] ASAMI T,NISHIHARA O. Analytical and experimental evaluation of an air damped dynamic vibration absorber:design optimizations of the three-element type model[J].Journal of Vibration and Acoustics,1999,121:334-342.
[16] ASAMI T,NISHIHARA O. H2 optimization of the threeelement type dynamic vibration absorbers[J]. Journal of Vibration and Acoustics,2002,124:583-592.
[17] SHEN Y J, WANG L, YANG S P, et al. Nonlinear dynamical analysis and parameters optimization of four semiactive on-off dynamic vibration absorbers[J]. Journal of Vibration and Control,2013,19(1):143-160.
[18]SHEN Y J,AHMADIAN M. Nonlinear dynamical analysis on four semi-active dynamic vibration absorbers with time delay[J]. Shock and Vibration,2013,20(4):649-663.
[19] ALABUZHEV P M,RIVIN E I. Vibration protecting and measuring systems with quasi-zero stiffness[M]. New York:Hemisphere Pub. Corp,1989.
[20]PLATUS D L. Negative-stiffness-mechanism vibration isolation systems[J]. In:International Society for Optics and Photonics,1992,1619:44-54.
[21]彭献,陈树年.负刚度的工作原理及应用初探[J].湖南大学学报(自然科学版),1992,19(4):89-94.PENG Xian,CHEN Shunian. Research on theory of negative stiffness and its application[J]. Journal of Hunan University(Natural Seiences),1992,19(4):89-94.
[22]彭解华,陈树年.正负刚度并联结构的稳定性及应用研究[J].振动、测试与诊断,1995,15(2):14-18.PENG Jiehua,CHEN Shunian. The stability and application of a structure with positive stiffness element and negative stiffness element[J]. Journal of Vibration,Measurement&Diagnosis,1995,15(2):14-18.
[23] ACAR M A,YILMAZ C. Design of an adaptive-passive dynamic vibration absorber composed of a string-mass system equipped with negative stiffness tension adjusting mechanism[J]. Journal of Sound and Vibration,2013,332(2):231-245.
[24]彭海波,申永军,杨绍普.一种含负刚度元件的新型动力吸振器的参数优化[J].力学学报,2015,47(2):320-327.PENG Haibo,SHEN Yongjun,YANG Shaopu. Parameters optimization of a new type of dynamic vibration absorber with negative stiffness[J]. Chinese Journal of Theoretical and Applied Mechanics,2015,47(2):320-327.
[25]SHEN Y J,WANG X R,YANG S P,et al. Parameters optimization for a kind of dynamic vibration absorber with negative stiffness[J]. Mathematical Problems in Engineering,2016(4):1-10.
[26] ANTONIADIS I,CHRONOPOULOS D,SPITAS V,et al.Hyper-damping properties of a stiff and stable linear oscillator with a negative stiffness element[J]. Journal of Sound and Vibration,2015,346(1):37-52.