磁流变弹性体调谐动力吸振器优化设计
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摘要
振动是生产和生活中常见的现象。振动控制包括被动和主动振动控制,主要用于减少有害振动。近年来,振动主动控制在航空航天、船舶、汽车等工业领域已经得到了广泛的应用,振动及振动主动控制的理论也已经基本成熟。磁流变弹性体是电磁流变材料中重要分支,其典型特征是剪切模量可控,且响应快,可逆性好,可控能力强,不沉降、稳定性高。基于磁流变弹性体的磁流变效应,利用磁流变弹性体作为变刚度元件设计的半主动动力吸振器可以减小主系统的振动,具有广阔的工程应用前景。
本文首先介绍了吸振器的发展历史,研究现状和基于磁流变弹性体的调谐动力吸振技术的研究现状。随后分别从时域、频域和能量的角度分析了吸振器的工作原理及吸振器阻尼,动质量和主系统阻尼影响吸振器减振效果的机制。根据磁流变弹性体动态力学性能的特点,设计摆式磁流变弹性体调谐动力吸振器和磁流变弹性体动态调刚度动力吸振器。摆式磁流变弹性体调谐动力吸振器由对称的绕同一摆轴摆动的摆臂组成,其基于磁流变弹性体动态力学性能随应变量变化而变化的特点,通过减小相同动质量质心振幅下磁流变弹性体的剪切变形量,进而保证足够的相对磁流变效应和较小的损耗因子。磁流变弹性体动态调刚度动力吸振器基于磁流变效应和挤压增强效应,通过准静态励磁电流和导磁回路提供的励磁磁场控制磁流变弹性体的剪切模量,进而控制吸振器的准静态刚度,实现吸振器固有频率跟踪激励频率;通过压电驱动器动态调节磁流变弹性体的压缩量,进而动态调节磁流变弹性体的刚度。这种吸振器采用混合控制论动态刚度部分按开关控制律变化,由调谐控制率控制由磁场控制的准静态刚度;由开关控制率控制由压电陶瓷驱动的基于挤压增强作用的动态刚度部分。仿真结果表明,和普通调谐动力吸振器相比,磁流变弹性体动态调刚度动力吸振器能更有效地减小主系统的振动;磁流变弹性体挤压增强作用越大,减振效果越好。
It is well known that vibration is one of the most usual phenomenon in daily life. Vibration control, including passive vibration control and active vibration control, is designed to suppress nuisance vibration. In recent years, active vibration control techniques have been widely applied to many fields, such as aerospace industry, ships, automobiles and so on. Theories of vibration and active vibration control have also been developed. Magnetorheological elastomer (MRE) is a kind of smart materials. Its unique character is that its modulus could be controlled by the magnetic field reversely, quickly. This character makes it qualify as spring element with controllable stiffness in adaptive tuned vibration absorber and shows great promising applications.
In this paper, the development trace of dynamic absorber was introduced firstly, and adaptive tuned vibration absorber (ATVA) based on MRE is discussed in detail. Then, time domain analysis, frequency domain analysis and energy analysis were used to analyse the working principle of ATVA. Based on the dynamic mechanical property of MRE, two new kind adaptive tuned vibration absorbers were proposed. A pendulum-like ATVA based on MRE was first developed. The developed system has two axisymmetric pendulum arms swaying around the same pendulum axis. The MRE smart spring element is placed between pendulum arms and pendulum axis to connect these parts together. Its frequency-shift property and vibration absorption capacity were theoretically analyzed and experimentally evaluated by employing a beam with two ends supported. Both experimental and theoretical results demonstrate that the developed MRE based pendulum-like ATVA holds wide frequency-shift range and good vibration absorption capabilities. Comparing with the previous MRE based ATVA systems, the developed pendulum-like MRE ATVA decreases the dynamic strain of MRE and its viscous damping, ensures the shift-frequency range and enhances the vibration absorption capacity. A novel dynamic stiffness tuning vibration absorber working with MR elastomers is then developed. In this design, the MRE worked in a shear mode, but its MR effect was significantly enhanced by dynamically squeezing the sample thickness with an embedded piezoelectric (PZT) actuator. With this design, both the quasi-static magnetic field and the PZT driven dynamic squeeze strain in the direction of particles chain were properly adjusted to control the vibration of the primary system. The vibration suppression capabilities were theoretically analyzed by the harmonic analysis. A combined control strategy (the tuning strategy and the ON-OFF strategy) and the control system were developed to suppress the vibration of the primary system. The simulation results indicate that the proposed MRE-PZT based DSTDVA exhibits more effective suppression capabilities than those conventional MRE based quasi-static tuned vibration absorbers; the stronger the enhancing effect of squeeze strain on MRE’s shear storage modulus is, the more effective vibration suppression capabilities the proposed MRE-PZT based DSTDVA has.
本文首先介绍了吸振器的发展历史,研究现状和基于磁流变弹性体的调谐动力吸振技术的研究现状。随后分别从时域、频域和能量的角度分析了吸振器的工作原理及吸振器阻尼,动质量和主系统阻尼影响吸振器减振效果的机制。根据磁流变弹性体动态力学性能的特点,设计摆式磁流变弹性体调谐动力吸振器和磁流变弹性体动态调刚度动力吸振器。摆式磁流变弹性体调谐动力吸振器由对称的绕同一摆轴摆动的摆臂组成,其基于磁流变弹性体动态力学性能随应变量变化而变化的特点,通过减小相同动质量质心振幅下磁流变弹性体的剪切变形量,进而保证足够的相对磁流变效应和较小的损耗因子。磁流变弹性体动态调刚度动力吸振器基于磁流变效应和挤压增强效应,通过准静态励磁电流和导磁回路提供的励磁磁场控制磁流变弹性体的剪切模量,进而控制吸振器的准静态刚度,实现吸振器固有频率跟踪激励频率;通过压电驱动器动态调节磁流变弹性体的压缩量,进而动态调节磁流变弹性体的刚度。这种吸振器采用混合控制论动态刚度部分按开关控制律变化,由调谐控制率控制由磁场控制的准静态刚度;由开关控制率控制由压电陶瓷驱动的基于挤压增强作用的动态刚度部分。仿真结果表明,和普通调谐动力吸振器相比,磁流变弹性体动态调刚度动力吸振器能更有效地减小主系统的振动;磁流变弹性体挤压增强作用越大,减振效果越好。
It is well known that vibration is one of the most usual phenomenon in daily life. Vibration control, including passive vibration control and active vibration control, is designed to suppress nuisance vibration. In recent years, active vibration control techniques have been widely applied to many fields, such as aerospace industry, ships, automobiles and so on. Theories of vibration and active vibration control have also been developed. Magnetorheological elastomer (MRE) is a kind of smart materials. Its unique character is that its modulus could be controlled by the magnetic field reversely, quickly. This character makes it qualify as spring element with controllable stiffness in adaptive tuned vibration absorber and shows great promising applications.
In this paper, the development trace of dynamic absorber was introduced firstly, and adaptive tuned vibration absorber (ATVA) based on MRE is discussed in detail. Then, time domain analysis, frequency domain analysis and energy analysis were used to analyse the working principle of ATVA. Based on the dynamic mechanical property of MRE, two new kind adaptive tuned vibration absorbers were proposed. A pendulum-like ATVA based on MRE was first developed. The developed system has two axisymmetric pendulum arms swaying around the same pendulum axis. The MRE smart spring element is placed between pendulum arms and pendulum axis to connect these parts together. Its frequency-shift property and vibration absorption capacity were theoretically analyzed and experimentally evaluated by employing a beam with two ends supported. Both experimental and theoretical results demonstrate that the developed MRE based pendulum-like ATVA holds wide frequency-shift range and good vibration absorption capabilities. Comparing with the previous MRE based ATVA systems, the developed pendulum-like MRE ATVA decreases the dynamic strain of MRE and its viscous damping, ensures the shift-frequency range and enhances the vibration absorption capacity. A novel dynamic stiffness tuning vibration absorber working with MR elastomers is then developed. In this design, the MRE worked in a shear mode, but its MR effect was significantly enhanced by dynamically squeezing the sample thickness with an embedded piezoelectric (PZT) actuator. With this design, both the quasi-static magnetic field and the PZT driven dynamic squeeze strain in the direction of particles chain were properly adjusted to control the vibration of the primary system. The vibration suppression capabilities were theoretically analyzed by the harmonic analysis. A combined control strategy (the tuning strategy and the ON-OFF strategy) and the control system were developed to suppress the vibration of the primary system. The simulation results indicate that the proposed MRE-PZT based DSTDVA exhibits more effective suppression capabilities than those conventional MRE based quasi-static tuned vibration absorbers; the stronger the enhancing effect of squeeze strain on MRE’s shear storage modulus is, the more effective vibration suppression capabilities the proposed MRE-PZT based DSTDVA has.
引文
[1]倪振华, 1986.振动力学.西安:西安交通大学出版社。
[2]顾仲权,马扣根,陈卫东, 1997.振动主动控制.北京:国防工业出版社。
[3] Frahm H., 1911, "Device for Damping Vibration of Bodies", US patent: 989958.
[4] Arnold F.R.,1955,"Steady-State Behaviour of Systems Provided with Non-linear DVA", Journal of Applied Mechanics, Vol.22.
[5] Rice H.J., 1987, "Practical Non-lineaar Vibration Absorber Design", Journal of Sound and Vibration, Vol.116.
[6] Verdirame J. and Nayfeh S., 2003, "Design of multi-degree-of-freedom tuned mass dampersbased on eigenvalue perturbation", 44th Structures, Structural Dynamics and Materials conference.
[7] Zou L. and Nayfeh S. A., 2004, "Minimac optimization of multio-degree-of-freedom tuned-mass dampers", Journal of Sound and Vibration, Vol.272:893-908.
[8] Zou L. and Nayfeh S. A., 2006, "The two-degree-of-freedom tuned-mass damper for suppression of singal-mode vibration under random and harmonic excitation", Journal of Vibration and Acoustics, Vol.128 (1):56-65.
[9] Snowdon J.C., 1974, "Dynamic Vibration Absorber That Have Increased Effectiveness", Journal of Engineering for Industry, Vol.96.
[10] Kazuto Seto, 1982, "An Investigaton of the Vibration Isolatro Equipped with Dual Dynamic Dampers as a Damping Element, Ist Repaot, Optimum Adjustment Condition for Dual Dynamic Dampers", The Japan Society of Mechanical Engineers, Vol. 24 (197):2013-2019.
[11] Jacquot R. G. and Foster J. E., 1977, "Optimal cantilever dynamic vibration absorber", Journal of Engineering for Industry, Vol.99:138-141.
[12] Snowdon J. C., Wolfe A. A. and Kerlin R. L., 1984, "The cruciform dynamic absorber", Journal of the Acoustical Society of America, Vol.75:1792-1799.
[13] Dahlbe T., 1989, "On optimal use of the mass of a dynamic vibration absorber", Journal of Sound and Vibration, Vol.132:518-522.
[14] Shin Y. S., Watson S. J. and Kim K. S., 1993, "Passive vibration control scheme using circular viscoelastic waveguide absorbers", Journal of Pressure Vessel Technology, Vol.115:256-261.
[15] Oniszczuk Z., 2003, "Damped vibration analysis of an elastically connected double-string complex system", Journal of Sound and Vibration, Vol.264: 253-271.
[16] Oniszczuk Z., 1999, "Transverse vibrations of elastically connected rectangular double-membrane compound system", Journal of Sound and Vibration, Vol.221:235-250.
[17] Aida T., Aso T. and Nakamoto K., 1998, "Vibration control of shallow shell structures using a shell-type dynamic vibration absorber", Journal of Sound and Vibration, Vol.218:245-267.
[18] Ormondroyd J. and Denhartog J.P., 1928, "Theory of the Dynamic Vibration Absorber", Trans. ASME, Vol.50.
[19] Brock J.E., 1946, "A note on the damped vibration absorber", J Journal of Applied Mechanics, Vol.68: A-284.
[20] Randil S.E., Halsted D.M. and Taylor D.L., 1981, "Optimal Vibration Absorber for Linear Damped System", Journal of Mechanical Design, Vol.103:908-913.
[21] Ng C. and Cunniff P. F., 1974, "Optimization of Mechanical Vibration Isolation System with Multi-Degree of Freedom", Journal of Sound and Vibration, Vol. 36.
[22]伍良生,顾仲权, 1994, "阻尼动力吸振器减振问题的进一步研究",振动与冲击,Vol.1:1-7.
[23]伍良生,顾仲权, 1990, "具有多个主振模态振动系统得减振优化设计",振动工程学报, Vol.3:18-24.
[24]张洪田,李玩幽,刘志刚, 2001"电动式主动吸振技术研究",振动工程学报, Vol.14 (1):113-117.
[25] Jalili N. and Knowles D.W. 2004 "Structural vibration control using an active resonator absorber: modeling and control implementation", Smart Materials and Structures, Vol.13 (5)998-1005.
[26] Olgac N. and Jalili. N., 1998 "Modal analysis of flexible beams with delayed resonator vibration absorber: theory and experiments" Journal of Sound and Vibration, Vol.218 (2)307-331.
[27] Filipovic D. and Schroder D., 1998 "Bandpass vibration absorber", Journal of Sound and Vibration, Vol.214 (3):553-566.
[28] Walsh P. L. and Lamancusa J. S., 1992 "A variable stiffness vibration absorber for minimization of transient vibrations", Journal of Sound and Vibration, Vol.158 (2):195 -211.
[29] Nagaya K. and Kurusu A., 1999, "Vibration control of a structure by using a tunable absorber and an optimal vibration absorber under autotuning control", Journal of Sound and Vibration, Vol.228 (4):773-792.
[30] Hill S.G. and Snyder S.D., 2002, "Design of an adaptive vibration absorber to reduce electrical transformer structural vibration", Journal of Vibration and Acoustics, Vol.124 (4):606-611.
[31] Nagarajaiah S. and Varadarajan N., 2005, "Short time Fourier transform algorithm for wind response control of buildings with variable stiffness TMD", Engineering Structures, Vol.27 (3):431-441.
[32] Yong C., Zimcik D. G., Wickramasinghe V. K. and Nitzsche F., 2004, "Development of the smart spring for active vibration control of helicopter blades", Journal of Intelligent Material Systems and Structures, Vol.15 (1):37-47.
[33] Davis C. L., Lesieutre G. A. and Dosch J., 1995, "A Tunable Electrically Shunted Piezoceramic Vibration Absorber", Proc.SPIE, Vol.3045: 51–59.
[34] Davis C. L. and Lesieutre G. A., 2000, "An Actively Tuned Solid-State Vibration Absorber Using Capacitive Shunting of Piezoelectric Stiffness", Journal of Sound and Vibration, Vol.232 (3): 601–617.
[35] Williams K., Chiu G. and Bernhard R., 2002, "Adaptive-passive absorbers using shape-memory alloys", Journal of Sound and Vibration, Vol.249 (5):835-848.
[36] Williams K. A., Chiu G. T. C. and Bernhard R.J., 2005, "Dynamic modelling of a shape memory alloy adaptive tuned vibration absorber", Journal of Sound and Vibration, Vol.280:211-234.
[37] Rustighi E., Brennan M.J. and Mace B.R., 2005, "Real-time control of a shape memory alloy adaptive tuned vibration absorber", Smart Materials and Structures, Vol.14:1184-1195.
[38] Holdhusen M. H., 2005, "The state-switched absorber used for vibration control of continuous systems", Ph D thesis, Georgia Institute of Technology.
[39] Ginder J. M. and Nichols M. E., 1999, "Magnetorheological Elastomers: Properties and Applications", Proceedings of SPIE, Vol.3675:131-138.
[40] Ginder J. M., Nichols M. E. and Elie L. D., 2000, "Controllable-Stiffness Components Based on Magnetorheological Elastomers", Proceedings of SPIE, Vol.3985: 418-425.
[41] Ginder J. M., Schlotter W. F. and Nichols M. E., 2001, "Magnetorheological Elastomers in Tunable Vibration Absorbers", Proceedings of SPIE, Vol.4331:103-110.
[42] Lerner A.A. and Cunefare K.A., 2008, ''Performance of MRE-Based Vibration Absorbers'', Journal of Intelligent Material Systems and Structures, Vol.19 (5): 551-565.
[43] Franchek, M. A. Ryan, M. W. and Bernhard, R. J., 1996, ''Adaptive Passive Vibration Control'', Journal of Sound and Vibration, Vol.189 (5): 565–585.
[44] Nagaya K., Kurusu A., Ikai S. and Shitani Y., 1999, "Vibration control of a structure by using a tunable absorber and an optimal vibration absorber under auto-tuning control" Journal of Sound and Vibration, Vol.228 (4):773-792.
[45] Buhr C., Franchek M. A., and Bernhard R.J., 1997, "Non-collocated adaptive-passive vibration control", Journal of Sound and Vibration, Vol.206:371-398.
[46] Kidner M. R. F. and Brennan, M. J., 2002, "Varying the Stiffness of a Beam-Like Neutralizer Under Fuzzy Logic Control", Journal of Vibration and Acoustics, Vol.124(1): 90-99.
[47] Kidner M. R. F., Brennan M. J.“Real-time control of both stiffness and damping in an active vibration neutralizer”Smart Structures and materials, 2001, 10(4): 758-769.
[48] Winslow W. M., 1947, "Translating Electrical Impulses into Mechanical Force", U. S. Patent 2,417,850.
[49] Winslow W. M., 1949, "Induced Fibration of Suspensions", Journal of Applied Physics, Vol.20:1137-1140.
[50] Rabinow J., 1948, "Magnetic Fluid Clutch", Technical News Bulletin, National Bureau of Standards, Vol.32 (4):54-60.
[51] Rabinow J., 1948, "The Magnetic Fluid Clutch", AIEE Transactions, Vol.67:1308-1315.
[52] Jolly M. R., Bender J. W. and Carlson J. D., 1999, "Properties and Applications of Commercial110 Magnetorheological Fluids", Journal of Intelligent Material Systems and Structures, Vol.10 (1):5-13.
[53] Shiga T., Okada A., and Kurauchi T., 1995, "Magnetroviscoelastic Behavior of Composite Gels", Journal of Applied Polymer Science, Vol.58: 787-792.
[54] Jolly M. R. and Carlson J. D., 1996, "The Magnetoviscoelastic Response of Elastomer Composites Consistings of Ferrous Particles Embedded in a Polymer Matrix", Journal of Intelligent Material Systems and Structures, Vol.7: 613-622.
[55] Ginder J. M. and Nichols M. E., 1999, "Magnetorheological Elastomers: Properties and Applica-tions", Smart Materials Technologies, Proceedings of SPIE, Vol.3675: 131-138.
[56] Davis L. C., 1999, "Model of Magnetorheological Elastomers", Journal of Applied Physics, Vol.85: 3348-3351.
[57] Bossis G., 2001, "Electroactive and Electrostructured Elastomers", Journal of Modern Physics B, Vol.15: 564-573.
[58] Bednarek S., 1999, "The Giant Magnetostriction in Ferromagnetic Composites within an Elastomer Matrix", Applied Physics A, Vol.68: 63-67.
[59] Demchuk S. A. and Kuz’min V. A., 2002, "Viscoelastic Properties of Magnetorheological Elastomers in the Regime of Dynamic Deformation", Journal of Engineering Physics and Thermophysics, Vol.75: 396-400.
[60] Lokander M. and Stenberg B., 2003, "Performance of Isotropic Magnetorheological Rubber Materials", Polymer Testing, Vol.22: 245-251.
[61] Lokander M. and Stenberg B., 2003, "Improving the Magnetorheological Effect in Isotropic Magneto- rheoligcal Rubber Materials", Polymer Testing, Vol.22: 677-680.
[62] Shen Y., Golnaraghi M. F. and Heppler G. R., 2004, "Experimental Research and Modeling of Magnetorheological Elastomers", Journal of intelligent material systems and structures, Vol.15: 27-35.
[63] Blom P. and Kari L., 2005, "Amplitude and Frequency Dependence of Magneto-Sensitive Rubber in A Wide Frequency Range", Polymer Testing, Vol.24: 656–662.
[64] Watson J. R., 1997, "Method and Apparatus for Varying the Stiffness of a Suspension Bushing”, U.S. Patent, 5609353.
[65] Ginder J. M., Schlotter W. F. and Nichols M. E., 2001, "Magnetorheological Elastomers in Tunable Vibration Absorbers", Proceedings of SPIE, Vol.4331: 103-110.
[66] Albanese A. M. and Cunefare K. A., 2003, "The Temporal and Spatial Effects of a Magnetorheological Elastomer in Squeeze Mode", Acoustical Society of America Journal, Vol.114 (4): 2419-2419.
[67] Albanese A. M. and Cunefare K. A., 2003, "Properties of A Magnetorheological Semiactive Vibration Absorber", Proceedings of SPIE, Vol.5052: 36-43.
[68] Albanese A. M. and Cunefare K. A., 2006, "Adaptable Vibration Absorber Employing A Magneto-Rheological Elastomer with Variable Gap Length and Methods and Systems Therefore", US patent 7,102,474 B2.
[69] H.X.Deng, X.L.Gong and L.H.Wang., 2006, "Development of an Adaptive Tuned Vibration Absorber with Magnetorheological Elastomer", Smart Materials and Structures, Vol.15: 111–116。
[70] H.X.Deng and X.L.Gong, 2008, "Application of Magnetorheological Elastomer to Vibration Absorber", Journal of Communications in Nonlinear Science and Numerical Simulation,Vol.13 (9):1938-1947.
[71] H.X.Deng and X.L.Gong, 2007, "Adaptive Tuned Vibration Absorber Based on Magnetorheological Elastomer", Journal of intelligent material systems and structures, Vol.18 (12): 1205-1210.
[72] Li, W. H., Chen, G., and Yeo, S.H., 1999 ''Viscoelastic Properties of MR Fluids,'' Smart Materials and Structures, Vol.8 (4):460-468.
[73] Gong X. L, Chen L. and Li J. F., 2007, "Study of Utilizable Magnetorheological Elastomers", Journal of Intelligent Material Systems and Structures, Vol.18 (12):1205-1210.
[74] Xianzhou Zhang, Xinglong Gong, Peiqiang Zhang and Qiming Wang, 2004, "Study on mechanism of squeeze-strengthen effect in magnetorheological fluids", Journal of Applied Physics, Vol.96 (4):2359-2364.
[75] Sun H. L., Zhang P. Q., Gong X. L. and Chen H. B., 2007,"A novel kind of active resonator absorber and the simulation on its control effort", Journal of Sound and Vibration, Vol.300 :117–125
[76] Ginder J. M., Schlotter W. F. and Nichols, M. E., 2001, ''Magnetorheological Elastomers in Tunable Vibration Absorbers,'' Proc. SPIE, Vol.4331:103-110.
[77] Deng H. X. and Gong X. L. 2007. ''Adaptive Tuned Vibration Absorber Based on Magnetorheological Elastomer,'' Journal of Intelligent Material Systems and Structures, Vol.18 (12): 1205-1210.
[78] Lerner, A. A. and Cunefare, K. A., 2008, ''Performance of MRE-Based Vibration Absorbers,'' Journal of Intelligent Material Systems and Structures, Vol.19 (5): 551-565.
[79] Franchek M. A., Ryan, M. W. and Bernhard, R. J. 1996, ''Adaptive Passive Vibration Control'', Journal of Sound and Vibration, Vol.189 (5): 565-585.
[80] Buhr C., Franchek M. A. and Bernhard R. J., 1997. ''Non-Collocated Adaptive–Passive Vibration Control'', Journal of Sound and Vibration, Vol.206 (3):371-398.
[81] Hill S. G. and Snyder S. D., 2002, ''Design of an Adaptive Vibration Absorber to Reduce Electrical Transformer Structural Vibration'', Journal of Vibration and Acoustics, Vol.124 (4): 606-611.
[82] Rustighi E., Brennan M. J. and Mace B. R., 2005, ''Real-Time Control of a Shape Memory Alloy Adaptive Tuned Vibration Absorber'', Smart Materials and Structures, Vol.14 (6):1184-119.
[83] Kidner M. R. F. and Brennan M. J., 1999, ''Improving the performance of a vibration neutralizer by actively removing damping'', Journal of Sound and Vibration, Vol.221:587–606.
[84] Kidner M. R. F. and Brennan M. J., 2001, ''Real-time Control of Both Stiffness and Damping in An Active Vibration Neutralizer'', Smart Structures and materials, Vol.10:758-769. Wu S. T. and Shao Y. J., 2007, ''Adaptive vibration control using a virtual-vibration-absorber controller'', Journal of Sound and Vibration, Vol.305: 891-903.
[2]顾仲权,马扣根,陈卫东, 1997.振动主动控制.北京:国防工业出版社。
[3] Frahm H., 1911, "Device for Damping Vibration of Bodies", US patent: 989958.
[4] Arnold F.R.,1955,"Steady-State Behaviour of Systems Provided with Non-linear DVA", Journal of Applied Mechanics, Vol.22.
[5] Rice H.J., 1987, "Practical Non-lineaar Vibration Absorber Design", Journal of Sound and Vibration, Vol.116.
[6] Verdirame J. and Nayfeh S., 2003, "Design of multi-degree-of-freedom tuned mass dampersbased on eigenvalue perturbation", 44th Structures, Structural Dynamics and Materials conference.
[7] Zou L. and Nayfeh S. A., 2004, "Minimac optimization of multio-degree-of-freedom tuned-mass dampers", Journal of Sound and Vibration, Vol.272:893-908.
[8] Zou L. and Nayfeh S. A., 2006, "The two-degree-of-freedom tuned-mass damper for suppression of singal-mode vibration under random and harmonic excitation", Journal of Vibration and Acoustics, Vol.128 (1):56-65.
[9] Snowdon J.C., 1974, "Dynamic Vibration Absorber That Have Increased Effectiveness", Journal of Engineering for Industry, Vol.96.
[10] Kazuto Seto, 1982, "An Investigaton of the Vibration Isolatro Equipped with Dual Dynamic Dampers as a Damping Element, Ist Repaot, Optimum Adjustment Condition for Dual Dynamic Dampers", The Japan Society of Mechanical Engineers, Vol. 24 (197):2013-2019.
[11] Jacquot R. G. and Foster J. E., 1977, "Optimal cantilever dynamic vibration absorber", Journal of Engineering for Industry, Vol.99:138-141.
[12] Snowdon J. C., Wolfe A. A. and Kerlin R. L., 1984, "The cruciform dynamic absorber", Journal of the Acoustical Society of America, Vol.75:1792-1799.
[13] Dahlbe T., 1989, "On optimal use of the mass of a dynamic vibration absorber", Journal of Sound and Vibration, Vol.132:518-522.
[14] Shin Y. S., Watson S. J. and Kim K. S., 1993, "Passive vibration control scheme using circular viscoelastic waveguide absorbers", Journal of Pressure Vessel Technology, Vol.115:256-261.
[15] Oniszczuk Z., 2003, "Damped vibration analysis of an elastically connected double-string complex system", Journal of Sound and Vibration, Vol.264: 253-271.
[16] Oniszczuk Z., 1999, "Transverse vibrations of elastically connected rectangular double-membrane compound system", Journal of Sound and Vibration, Vol.221:235-250.
[17] Aida T., Aso T. and Nakamoto K., 1998, "Vibration control of shallow shell structures using a shell-type dynamic vibration absorber", Journal of Sound and Vibration, Vol.218:245-267.
[18] Ormondroyd J. and Denhartog J.P., 1928, "Theory of the Dynamic Vibration Absorber", Trans. ASME, Vol.50.
[19] Brock J.E., 1946, "A note on the damped vibration absorber", J Journal of Applied Mechanics, Vol.68: A-284.
[20] Randil S.E., Halsted D.M. and Taylor D.L., 1981, "Optimal Vibration Absorber for Linear Damped System", Journal of Mechanical Design, Vol.103:908-913.
[21] Ng C. and Cunniff P. F., 1974, "Optimization of Mechanical Vibration Isolation System with Multi-Degree of Freedom", Journal of Sound and Vibration, Vol. 36.
[22]伍良生,顾仲权, 1994, "阻尼动力吸振器减振问题的进一步研究",振动与冲击,Vol.1:1-7.
[23]伍良生,顾仲权, 1990, "具有多个主振模态振动系统得减振优化设计",振动工程学报, Vol.3:18-24.
[24]张洪田,李玩幽,刘志刚, 2001"电动式主动吸振技术研究",振动工程学报, Vol.14 (1):113-117.
[25] Jalili N. and Knowles D.W. 2004 "Structural vibration control using an active resonator absorber: modeling and control implementation", Smart Materials and Structures, Vol.13 (5)998-1005.
[26] Olgac N. and Jalili. N., 1998 "Modal analysis of flexible beams with delayed resonator vibration absorber: theory and experiments" Journal of Sound and Vibration, Vol.218 (2)307-331.
[27] Filipovic D. and Schroder D., 1998 "Bandpass vibration absorber", Journal of Sound and Vibration, Vol.214 (3):553-566.
[28] Walsh P. L. and Lamancusa J. S., 1992 "A variable stiffness vibration absorber for minimization of transient vibrations", Journal of Sound and Vibration, Vol.158 (2):195 -211.
[29] Nagaya K. and Kurusu A., 1999, "Vibration control of a structure by using a tunable absorber and an optimal vibration absorber under autotuning control", Journal of Sound and Vibration, Vol.228 (4):773-792.
[30] Hill S.G. and Snyder S.D., 2002, "Design of an adaptive vibration absorber to reduce electrical transformer structural vibration", Journal of Vibration and Acoustics, Vol.124 (4):606-611.
[31] Nagarajaiah S. and Varadarajan N., 2005, "Short time Fourier transform algorithm for wind response control of buildings with variable stiffness TMD", Engineering Structures, Vol.27 (3):431-441.
[32] Yong C., Zimcik D. G., Wickramasinghe V. K. and Nitzsche F., 2004, "Development of the smart spring for active vibration control of helicopter blades", Journal of Intelligent Material Systems and Structures, Vol.15 (1):37-47.
[33] Davis C. L., Lesieutre G. A. and Dosch J., 1995, "A Tunable Electrically Shunted Piezoceramic Vibration Absorber", Proc.SPIE, Vol.3045: 51–59.
[34] Davis C. L. and Lesieutre G. A., 2000, "An Actively Tuned Solid-State Vibration Absorber Using Capacitive Shunting of Piezoelectric Stiffness", Journal of Sound and Vibration, Vol.232 (3): 601–617.
[35] Williams K., Chiu G. and Bernhard R., 2002, "Adaptive-passive absorbers using shape-memory alloys", Journal of Sound and Vibration, Vol.249 (5):835-848.
[36] Williams K. A., Chiu G. T. C. and Bernhard R.J., 2005, "Dynamic modelling of a shape memory alloy adaptive tuned vibration absorber", Journal of Sound and Vibration, Vol.280:211-234.
[37] Rustighi E., Brennan M.J. and Mace B.R., 2005, "Real-time control of a shape memory alloy adaptive tuned vibration absorber", Smart Materials and Structures, Vol.14:1184-1195.
[38] Holdhusen M. H., 2005, "The state-switched absorber used for vibration control of continuous systems", Ph D thesis, Georgia Institute of Technology.
[39] Ginder J. M. and Nichols M. E., 1999, "Magnetorheological Elastomers: Properties and Applications", Proceedings of SPIE, Vol.3675:131-138.
[40] Ginder J. M., Nichols M. E. and Elie L. D., 2000, "Controllable-Stiffness Components Based on Magnetorheological Elastomers", Proceedings of SPIE, Vol.3985: 418-425.
[41] Ginder J. M., Schlotter W. F. and Nichols M. E., 2001, "Magnetorheological Elastomers in Tunable Vibration Absorbers", Proceedings of SPIE, Vol.4331:103-110.
[42] Lerner A.A. and Cunefare K.A., 2008, ''Performance of MRE-Based Vibration Absorbers'', Journal of Intelligent Material Systems and Structures, Vol.19 (5): 551-565.
[43] Franchek, M. A. Ryan, M. W. and Bernhard, R. J., 1996, ''Adaptive Passive Vibration Control'', Journal of Sound and Vibration, Vol.189 (5): 565–585.
[44] Nagaya K., Kurusu A., Ikai S. and Shitani Y., 1999, "Vibration control of a structure by using a tunable absorber and an optimal vibration absorber under auto-tuning control" Journal of Sound and Vibration, Vol.228 (4):773-792.
[45] Buhr C., Franchek M. A., and Bernhard R.J., 1997, "Non-collocated adaptive-passive vibration control", Journal of Sound and Vibration, Vol.206:371-398.
[46] Kidner M. R. F. and Brennan, M. J., 2002, "Varying the Stiffness of a Beam-Like Neutralizer Under Fuzzy Logic Control", Journal of Vibration and Acoustics, Vol.124(1): 90-99.
[47] Kidner M. R. F., Brennan M. J.“Real-time control of both stiffness and damping in an active vibration neutralizer”Smart Structures and materials, 2001, 10(4): 758-769.
[48] Winslow W. M., 1947, "Translating Electrical Impulses into Mechanical Force", U. S. Patent 2,417,850.
[49] Winslow W. M., 1949, "Induced Fibration of Suspensions", Journal of Applied Physics, Vol.20:1137-1140.
[50] Rabinow J., 1948, "Magnetic Fluid Clutch", Technical News Bulletin, National Bureau of Standards, Vol.32 (4):54-60.
[51] Rabinow J., 1948, "The Magnetic Fluid Clutch", AIEE Transactions, Vol.67:1308-1315.
[52] Jolly M. R., Bender J. W. and Carlson J. D., 1999, "Properties and Applications of Commercial110 Magnetorheological Fluids", Journal of Intelligent Material Systems and Structures, Vol.10 (1):5-13.
[53] Shiga T., Okada A., and Kurauchi T., 1995, "Magnetroviscoelastic Behavior of Composite Gels", Journal of Applied Polymer Science, Vol.58: 787-792.
[54] Jolly M. R. and Carlson J. D., 1996, "The Magnetoviscoelastic Response of Elastomer Composites Consistings of Ferrous Particles Embedded in a Polymer Matrix", Journal of Intelligent Material Systems and Structures, Vol.7: 613-622.
[55] Ginder J. M. and Nichols M. E., 1999, "Magnetorheological Elastomers: Properties and Applica-tions", Smart Materials Technologies, Proceedings of SPIE, Vol.3675: 131-138.
[56] Davis L. C., 1999, "Model of Magnetorheological Elastomers", Journal of Applied Physics, Vol.85: 3348-3351.
[57] Bossis G., 2001, "Electroactive and Electrostructured Elastomers", Journal of Modern Physics B, Vol.15: 564-573.
[58] Bednarek S., 1999, "The Giant Magnetostriction in Ferromagnetic Composites within an Elastomer Matrix", Applied Physics A, Vol.68: 63-67.
[59] Demchuk S. A. and Kuz’min V. A., 2002, "Viscoelastic Properties of Magnetorheological Elastomers in the Regime of Dynamic Deformation", Journal of Engineering Physics and Thermophysics, Vol.75: 396-400.
[60] Lokander M. and Stenberg B., 2003, "Performance of Isotropic Magnetorheological Rubber Materials", Polymer Testing, Vol.22: 245-251.
[61] Lokander M. and Stenberg B., 2003, "Improving the Magnetorheological Effect in Isotropic Magneto- rheoligcal Rubber Materials", Polymer Testing, Vol.22: 677-680.
[62] Shen Y., Golnaraghi M. F. and Heppler G. R., 2004, "Experimental Research and Modeling of Magnetorheological Elastomers", Journal of intelligent material systems and structures, Vol.15: 27-35.
[63] Blom P. and Kari L., 2005, "Amplitude and Frequency Dependence of Magneto-Sensitive Rubber in A Wide Frequency Range", Polymer Testing, Vol.24: 656–662.
[64] Watson J. R., 1997, "Method and Apparatus for Varying the Stiffness of a Suspension Bushing”, U.S. Patent, 5609353.
[65] Ginder J. M., Schlotter W. F. and Nichols M. E., 2001, "Magnetorheological Elastomers in Tunable Vibration Absorbers", Proceedings of SPIE, Vol.4331: 103-110.
[66] Albanese A. M. and Cunefare K. A., 2003, "The Temporal and Spatial Effects of a Magnetorheological Elastomer in Squeeze Mode", Acoustical Society of America Journal, Vol.114 (4): 2419-2419.
[67] Albanese A. M. and Cunefare K. A., 2003, "Properties of A Magnetorheological Semiactive Vibration Absorber", Proceedings of SPIE, Vol.5052: 36-43.
[68] Albanese A. M. and Cunefare K. A., 2006, "Adaptable Vibration Absorber Employing A Magneto-Rheological Elastomer with Variable Gap Length and Methods and Systems Therefore", US patent 7,102,474 B2.
[69] H.X.Deng, X.L.Gong and L.H.Wang., 2006, "Development of an Adaptive Tuned Vibration Absorber with Magnetorheological Elastomer", Smart Materials and Structures, Vol.15: 111–116。
[70] H.X.Deng and X.L.Gong, 2008, "Application of Magnetorheological Elastomer to Vibration Absorber", Journal of Communications in Nonlinear Science and Numerical Simulation,Vol.13 (9):1938-1947.
[71] H.X.Deng and X.L.Gong, 2007, "Adaptive Tuned Vibration Absorber Based on Magnetorheological Elastomer", Journal of intelligent material systems and structures, Vol.18 (12): 1205-1210.
[72] Li, W. H., Chen, G., and Yeo, S.H., 1999 ''Viscoelastic Properties of MR Fluids,'' Smart Materials and Structures, Vol.8 (4):460-468.
[73] Gong X. L, Chen L. and Li J. F., 2007, "Study of Utilizable Magnetorheological Elastomers", Journal of Intelligent Material Systems and Structures, Vol.18 (12):1205-1210.
[74] Xianzhou Zhang, Xinglong Gong, Peiqiang Zhang and Qiming Wang, 2004, "Study on mechanism of squeeze-strengthen effect in magnetorheological fluids", Journal of Applied Physics, Vol.96 (4):2359-2364.
[75] Sun H. L., Zhang P. Q., Gong X. L. and Chen H. B., 2007,"A novel kind of active resonator absorber and the simulation on its control effort", Journal of Sound and Vibration, Vol.300 :117–125
[76] Ginder J. M., Schlotter W. F. and Nichols, M. E., 2001, ''Magnetorheological Elastomers in Tunable Vibration Absorbers,'' Proc. SPIE, Vol.4331:103-110.
[77] Deng H. X. and Gong X. L. 2007. ''Adaptive Tuned Vibration Absorber Based on Magnetorheological Elastomer,'' Journal of Intelligent Material Systems and Structures, Vol.18 (12): 1205-1210.
[78] Lerner, A. A. and Cunefare, K. A., 2008, ''Performance of MRE-Based Vibration Absorbers,'' Journal of Intelligent Material Systems and Structures, Vol.19 (5): 551-565.
[79] Franchek M. A., Ryan, M. W. and Bernhard, R. J. 1996, ''Adaptive Passive Vibration Control'', Journal of Sound and Vibration, Vol.189 (5): 565-585.
[80] Buhr C., Franchek M. A. and Bernhard R. J., 1997. ''Non-Collocated Adaptive–Passive Vibration Control'', Journal of Sound and Vibration, Vol.206 (3):371-398.
[81] Hill S. G. and Snyder S. D., 2002, ''Design of an Adaptive Vibration Absorber to Reduce Electrical Transformer Structural Vibration'', Journal of Vibration and Acoustics, Vol.124 (4): 606-611.
[82] Rustighi E., Brennan M. J. and Mace B. R., 2005, ''Real-Time Control of a Shape Memory Alloy Adaptive Tuned Vibration Absorber'', Smart Materials and Structures, Vol.14 (6):1184-119.
[83] Kidner M. R. F. and Brennan M. J., 1999, ''Improving the performance of a vibration neutralizer by actively removing damping'', Journal of Sound and Vibration, Vol.221:587–606.
[84] Kidner M. R. F. and Brennan M. J., 2001, ''Real-time Control of Both Stiffness and Damping in An Active Vibration Neutralizer'', Smart Structures and materials, Vol.10:758-769. Wu S. T. and Shao Y. J., 2007, ''Adaptive vibration control using a virtual-vibration-absorber controller'', Journal of Sound and Vibration, Vol.305: 891-903.