SOME RECENT PROGRESSES IN NONLINEAR PASSIVE ISOLATIONS OF VIBRATIONS

Lu Zeqi; Chen Liqun

doi:10.6052/0459-1879-17-064

Volume 49 Issue 3

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2017 > 49(3): 550-564

Lu Zeqi, Chen Liqun. SOME RECENT PROGRESSES IN NONLINEAR PASSIVE ISOLATIONS OF VIBRATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 550-564. doi: 10.6052/0459-1879-17-064

Citation:

Lu Zeqi, Chen Liqun. SOME RECENT PROGRESSES IN NONLINEAR PASSIVE ISOLATIONS OF VIBRATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 550-564. doi: 10.6052/0459-1879-17-064

Lu Zeqi, Chen Liqun. SOME RECENT PROGRESSES IN NONLINEAR PASSIVE ISOLATIONS OF VIBRATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 550-564. doi: 10.6052/0459-1879-17-064

Citation:

PDF( 6788 KB)

SOME RECENT PROGRESSES IN NONLINEAR PASSIVE ISOLATIONS OF VIBRATIONS

doi: 10.6052/0459-1879-17-064

Lu Zeqi^*,
Chen Liqun^{*, †
,
,}

*.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
†.
Department of Mechanics, Shanghai University, Shanghai 200444, China

Received Date: 2017-03-01
Available Online: 2017-04-21
Publish Date: 2017-05-18

Abstract

Abstract

Vibrations in aircraft and marine structures, due to various extreme environmental loads, have been attributing factors in accidents and failures. Over the last decade, as the demands for vibration and shock isolation performance increasing, the general approaches following the conventional categorization of passive, active, semi-active and hybrid has been extensive presented. Nonlinear passive vibration isolation is the state of the art of vibration control techniques for combining robustness of the passive device and high performance of the active devices. This paper surveys theoretical and practical advances in nonlinear passive isolation of vibration in recent ten years. Stiffness and damping both nonlinearities is considered in modeling of vibration isolation system; Deterministic and stochastic analysis are both conducted on the investigation of the dynamic behavior. Initially, a review of a general approach to quantify the effectiveness of nonlinear vibrations isolation is presented. This is then followed by a review of high-static-low-dynamic stiffness vibration isolation, damping nonlinearity vibration isolation, two-stage nonlinear vibration isolation and nonlinear vibration isolation materi-als. The other vibration isolation methods considered in this review include chaotic anti-control technology, influence of internal resonance and usage of nonlinear energy sink. The article is closed by conclusions, which highlight resolved and unresolved problems and recommendations for future research treads.
- vibration isolation,
- nonlinear vibration,
- high static low dynamic stiffness,
- nonlinear damping,
- isolation materials

FullText(HTML)

References(142)

References

[1]	Mead DJ, Meador D. Passive Vibration Control. Chichester:Wiley, 1998
[2]	Harris CM, Piersol AG. Harris' Shock and Vibration Handbook. New York:McGraw-Hill, 2002
[3]	Rivin EI. Passive Vibration Isolation, New York:ASME press, 2003
[4]	Fuller CC, Elliott S, Nelson PA. Active Control of Vibration. New York:Academic Press, 1996
[5]	Hansen C, Snyder S. Active Control of Noise and Vibration. London:E & FN Spon, 1997
[6]	Gawronski WK. Advanced Structural Dyanmaics and Active Control of Structures. New York:Springer, 2004
[7]	Ibrahim R. Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 2008. 314(3):371-452 https://www.researchgate.net/publication/253802068_Recent_advances_in_nonlinear_passive_vibration_isolators
[8]	Kovacic I, Brennan MJ. The Duffing Equation:Nonlinear Oscillators and Their Behaviour. UK:John Wiley & Sons, 2011
[9]	董瑶海.航天器微振动:理论与实践.北京:中国宇航出版社, 2015 Dong Yaohai. Micro-Vibration of Aircraft:Theoretic and Practice. Beijing:China Astronautic Publishing House, 2015 (in Chinese)
[10]	Kandasamy R, Cui F, Townsend N, et al. A review of vibration control methods for marine offshore structures. Ocean Engineering, 2016, 127:279-297 doi: 10.1016/j.oceaneng.2016.10.001
[11]	马兴瑞.动力学振动与控制新进展(航天技术专著).北京:中国宇航出版社, 2010 Ma Xingrui. Recent Advances in Dynamics Vibration and Control. Beijing:China Astronautic Publishing House, 2010 (in Chinese))
[12]	黄文虎, 曹登庆, 韩增尧.航天器动力学与控制的研究进展与展望.力学进展, 2012, 42(4):367-393 doi: 10.6052/1000-0992-11-171 Huang Wenhu, Cao Dengqing, Han Zengyao. Advances and trends in dynamics and control of spacecrafts. Advances in Mechanics, 2012, 42(4):367-393 (in Chinese) doi: 10.6052/1000-0992-11-171
[13]	Zheng G, Tu Y. Analytical study of vibration isolation between a pair of flexible structures. ASME Journal of Vibration and Acoustics, 2009, 31(6):1-10 http://xa.yimg.com/kq/groups/19679329/750550425/name/naresh+1.pdf
[14]	Zhang Y, Zhang J. Disturbances characteristics analysis of a control moment gyroscope due to imbalances and installation errors. IEEE Transactions on Aerospace and Electronic Systems, 2014, 50(2): 1017-1026 doi: 10.1109/TAES.2013.120543
[15]	Zhang Y, Zhang J, Xu S. Parameters design of vibration isolation platform for control moment gyroscopes. Acta Astronautica, 2012, 81(2):645-659 doi: 10.1016/j.actaastro.2012.08.031
[16]	Zhang Y, Zhang J, Xu S. Influence of flexible solar arrays on vibration isolation platform of control moment gyroscopes. Acta Mechanica Sinica, 2012, 28(5):1479-1487 doi: 10.1007/s10409-012-0148-x
[17]	Zhang Y, Zhang J, Zhai G. Vibration isolation platform with multiple tuned mass dampers for reaction wheel on satellites. Mathematical Problems in Engineering, 2013, 4:1-14 https://www.researchgate.net/profile/Jingrui_Zhang4/publication/258395511_Vibration_Isolation_Platform_with_Multiple_Tuned_Mass_Dampers_for_Reaction_Wheel_on_Satellites/links/56adabca08ae43a3980c8dd8.pdf?origin=publication_detail
[18]	Zhang Y, Zhang J. The imaging stability enhancement of optical payload using multiple vibration isolation platforms. Journal of Vibration and Control, 2013, 21(9):1848-1865 http://jvc.sagepub.com/content/21/9/1848.full.pdf
[19]	Zhang Y, Guo Z, He H, et al. A novel vibration isolation system for reaction wheel on space telescopes. Acta Astronautica, 2014, 102: 1-13 doi: 10.1016/j.actaastro.2014.05.014
[20]	Haritos N. Introduction to the analysis and design of offshore structures-an overview. Electronic Journal Structural Engineering, 2007, 7:55-65 http://www.ejse.org/Archives/Fulltext/2007/Special/200705.pdf
[21]	Bajkowski JM, Dyniewicz B, Bajer CI. Semi-active damping strategy for beams system with pneumatically controlled granular structure. Mechanical System and Signal Process, 2016, 70:387-396 https://www.researchgate.net/publication/282696108_Semi-active_damping_strategy_for_beams_system_with_pneumatically_controlled_granular_structure
[22]	Chakrabarti S. Handbook of Offshore Engineering. Oxford:Elsevier, 2015 https://www.elsevier.com/books/handbook-of-offshore-engineering-2-volume-set/chakrabarti/978-0-08-044381-2
[23]	Bargi K, Hosseini SR, Tadayon MH, et al. Seismic response of a typical fixed jacket-type offshore platform (spd1) under sea waves. Open Journal of Marine Science, 2011, 1(02):36 doi: 10.4236/ojms.2011.12004
[24]	Chandrasekaran S, Kumar D, Ramanathan R. Dynamic response of tension leg platform with tuned mass dampers. Journal of Naval Architecture and Marine Engineering, 2013, 10(2):149-156 https://www.researchgate.net/publication/287207615_Srinivasan_Chandrasekaran_Deepak_Kumar_and_Ranjani_Ramanathan_2013_Dynamic_response_of_tension_leg_platform_with_tuned_mass_dampers_Journal_of_Naval_Architecture_and_Marine_Engineering_Vol_10_No_2_pp_
[25]	Caterino N. Semi-active control of a wind turbine via magnetorheological damper. Journal ofSound and Vibration}, 2015, 345: 1-17 doi: 10.1016/j.jsv.2015.01.022
[26]	Lu Z, Brennan MJ, Chen L. On the transmissibilities of nonlinear vibration isolation system. Journal of Sound and Vibration, 2016, 375:28-37 doi: 10.1016/j.jsv.2016.04.032
[27]	Xie S, Or SW, Chan HLW, et al. Analysis of vibration power flow from a vibration machinery to a floating elastic panel. Michanical Systems and Signal Processing, 2007, 21:389-404 doi: 10.1016/j.ymssp.2005.11.004
[28]	Choi WJ, Xiong YP, Shenoi RA. Power flow analysis for a floating sandwich raft isolation system using a higher-order theory. Journal of Sound and Vibration, 2009, 319:228-246 doi: 10.1016/j.jsv.2008.05.020
[29]	Xing JT. Energy Flow Theory of Nonlinear Dynamical Systems with Applications. Switzerland:Springer, 2015 http://www.worldcat.org/title/energy-flow-theory-of-nonlinear-dynamical-systems-with-applications/oclc/910513140
[30]	马业忠, 霍睿.板式基础上非线性隔振系统的功率流传递特性.振动工程学报, 2008, 21(4):394-397 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200804014.htm Ma Yezhong, Huo Rui. Characteristic of power flow transmission in nonlinear vibration isolation system on plate base. Journal of Vibration Engineering, 2008, 21(4): 394-397 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC200804014.htm
[31]	高书磊, 霍睿.柔性基础上非线性隔振系统的动力学分析.振动与冲击, 2007, 26(6):113-116 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200706026.htm Gao Shulei, Huo Rui. Effect of nonlinear parameter of isolator on equipment's kinetic energy. Journal of Vibration and Shock, 2007, 26(6):113-116 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200706026.htm
[32]	Royston TJ, Singh R. Vibratory power flow through a nonlinear path into a resonant receiver. Journal of the Acoustical Society of America, 1997, 101:2059-2069 doi: 10.1121/1.418200
[33]	Xiong YP, Xing JT, Price WG. Interactive power flow characteristics of an integrated equipment-nonlinear isolator-travelling flexible ship excited by sea waves. Journal of Sound and Vibration, 2005, 287:245-276 doi: 10.1016/j.jsv.2004.11.009
[34]	Kerschen G, Peeters M, Golinval JC, et al. Nonlinear normal modes, Part I:a useful frame work for the structural dynamicist. Mechanical System and Signal Processing, 2009, 23:170-194 doi: 10.1016/j.ymssp.2008.04.002
[35]	Yang J, Xiong YP, Xing JT. Dynamics and power flow behavior of a nonlinear vibration isolation system with a negative stiffness mechanism. Journal of Sound and Vibration, 2013, 332:167-183 doi: 10.1016/j.jsv.2012.08.010
[36]	Yang J, Xiong YP, Xing JT. Nonlinear power flow analysis of the Duffing oscillator. Mechanical Systems and Signal Processing, 2014, 45:563-578 doi: 10.1016/j.ymssp.2013.11.004
[37]	Yang J, Xiong YP, Xing JT. Vibration power flow and force transmission behavior of a nonlinear isolator mounted on a nonlinear base. International Journal of Mechanical Sciences, 2016, 115-116: 238-252 doi: 10.1016/j.ijmecsci.2016.06.023
[38]	Ahn HJ. Performance limit of a passive vertical isolator using a negative stiffness mechanism. Journal of Mechanical Scinence and Technology, 2008, 22:2357-2367 doi: 10.1007/s12206-008-0930-7
[39]	Kim KR, You YH, Ahn HJ. Optimal design of a QZS isolator using flexures for a wide range of payload. International Journal of Precision Engineering and Manufacturing, 2013, 14(6):911-917 doi: 10.1007/s12541-013-0120-0
[40]	Robertson WS, Kidner MRF, Cazzolato BS, et al. Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation. Journal of Sound and Vibration, 2009, 326(1):88-103 https://www.researchgate.net/publication/222429068_Theoretical_design_parameters_for_a_quasi-zero_stiffness_magnetic_spring_for_vibration_isolation
[41]	Shin K. On the performance of a single degree-of-freedom highstatic-low-dynamic stiffness magnetic vibration isolator. International Journal of Precision Engineering and Manufacturing, 2014, 15(3):439-445 doi: 10.1007/s12541-014-0355-4
[42]	彭超, 龚兴龙, 宗路航等.新型非线性低频被动隔振系统设计及实验研究.振动与冲击, 2013, 32(3):6-11 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201303005.htm Peng Chao, Gong Xinglong, Zong Luhang, et al. Design and tests for a new type nonlinear low-frequency passive vibration isolation system. Journal of Vibration and Shock, 2013, 32(3):6-11 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201303005.htm
[43]	路纯红, 白鸿柏.新型超低频非线性被动隔振系统的设计.振动与冲击, 2011, 30(1):234-236 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201101056.htm Lu Chunhong, Bai Hongbai. A new type nonlinear ultra-low frequency passive vibration isolation system. Journal of Vibration and Shock, 2011, 30(1):234-236 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201101056.htm
[44]	Carrella A, Brennan MJ, Waters TP. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 2007, 301(3):678-689 https://www.researchgate.net/publication/241487262_Static_analysis_of_a_passive_vibration_isolator_with_Quasi-Zero_Stiffness_Characteristic
[45]	Kovacic I, Brennan MJ, Waters TP. A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. Journal of Sound and Vibration, 2008, 315:700-711 doi: 10.1016/j.jsv.2007.12.019
[46]	Carrella A, Brennan MJ, Kovacic I, et al. On the force transmissibility of a vibration isolator with quasi-zero-stiffness. Journal of Sound and Vibration, 2009, 322(4):707-717 https://www.researchgate.net/publication/253169106_On_the_force_transmissibility_of_a_vibration_isolator_with_quasi-zero-stiffness
[47]	Carrella A, Brennan MJ, Waters TP, et al. Force and displacement transmissibility of a nonlinear isolator with high-static-lowdynamic-stiffness. International Journal of Mechanical Sciences, 2012, 55(1):22-29 doi: 10.1016/j.ijmecsci.2011.11.012
[48]	Xu D, Yu Q, Zhou J, et al. Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 2013, 332:3377-3389 doi: 10.1016/j.jsv.2013.01.034
[49]	Sun X, Xu J, Jing X, et al. Beneficial performance of a quasi-zerostiffness vibration isolator with time-delayed active control. International Journal of Mechanical Science, 2014, 82:32-40 doi: 10.1016/j.ijmecsci.2014.03.002
[50]	Li Q, Zhu Y, Xu D, et al. A negative stiffness vibration isolator using magnetic spring combined with rubber membrane. Journal of Mechanical Scinece and Technology, 2013, 27(3):813-824 doi: 10.1007/s12206-013-0128-5
[51]	Huang X, Liu X, Hua H. On the characteristics of an ultra-low frequency nonlinear isolator using sliding beam as negative stiffness. Journal of Mechanical Science and Technology, 2014, 28(3):813-822 doi: 10.1007/s12206-013-1205-5
[52]	Huang X, Liu X, Sun J, et al. Effect of the system imperfections on the dynamic response of a high-static-low-dynamic stiffness vibration isolator. Nonlinear Dynamics, 2014, 76:1157-1167 doi: 10.1007/s11071-013-1199-7
[53]	Sun XT, Jing XJ, Xu J, et al. Vibration isolation via a scissor-like structured platform. Journal of Sound and Vibration, 2014, 333(9): 2404-2420 doi: 10.1016/j.jsv.2013.12.025
[54]	Zhang W, Zhao J. Analysis on nonlinear stiffness and vibration isolation performance of scissor-like structure with full types. Nonlinear Dynamics, 2016, 86:17-36 doi: 10.1007/s11071-016-2869-z
[55]	Friswell MI, Saavedra Flores EI. Dynamic isolation systems using tunable nonlinear stiffness beams. The European Physical Journal Special Topics, 2013, 222:1563-1573 doi: 10.1140/epjst/e2013-01945-5
[56]	Trung PV, Kim KR., Ahn HJ. A nonlinear control of an QZS isolator with flexures based on a Lyapunov function. International Journal of Precision Engineering and Manufacturing, 2013, 14(6):919-924 doi: 10.1007/s12541-013-0121-z
[57]	Le TD, Ahn KK. Fuzy sliding mode controller of a pneumatic active isolation system using negative stiffness structure. Journal of Mechanical Science and Technology, 2012, 26(12):3873-3884 doi: 10.1007/s12206-012-0890-9
[58]	Danh LT, Ahn KK. Active pneumatic vibration isolation system using negative stiffness structures for a vehicle seat. Journal of Sound and Vibration, 2014, 333(5):1245-1268 doi: 10.1016/j.jsv.2013.10.027
[59]	徐鉴.振动控制研究进展综述.力学季刊, 2015, 36(4):547-565 http://www.cnki.com.cn/Article/CJFDTOTAL-SHLX201504001.htm Xu Jian. Advances of research on vibration control. Chinese Quarterly of Mechanics, 2015, 36(4):547-565 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-SHLX201504001.htm
[60]	Xu J, Sun XT. A multi-directional vibration isolator based on quasizero-stiffness structure and time-delayed active control. International Journal of Mechanical Sciences, 2015, 100:126-135 doi: 10.1016/j.ijmecsci.2015.06.015
[61]	Sun XT, Jing XJ, Xu J, et al. A quasi-zero-stiffness-based sensor system in vibration measurement. IEEE Transactions on Industrial Electronics, 2014, 61(10):5606-5614 doi: 10.1109/TIE.2013.2297297
[62]	Sun XT, Jing XJ, Cheng L, et al. A 3D quasi-zero-stiffness based sensor system for absolute motion measurement and application in active vibration control. IEEE/ASME Transactions on Mechatronics, 2015, 20(1):254-262 doi: 10.1109/TMECH.2014.2338932
[63]	Zhou J, Xiao Q, Xu D, et al. A novel quasi-zero-stiffness strut and its applications in six-degree-of-freedom vibration isolation platform. Journal of Sound and Vibration, 2017, (in press) http://www.sciencedirect.com/science/article/pii/S0022460X17300445
[64]	Shaw A, Neild S, Wagg D, et al. A nonlinear spring mechanism incorporating a bistable composite plate for vibration isolation. Journal of Sound and Vibration, 2013, 332(24):6265-6275 doi: 10.1016/j.jsv.2013.07.016
[65]	Shaw A, Neild S, Wagg D. Dynamic analysis of high static low dynamic stiffness vibration isolation mounts. Journal of Sound and Vibration, 2013, 332(6):1437-1455 doi: 10.1016/j.jsv.2012.10.036
[66]	Le TD, Ahn KK. A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat. Journal of Sound and Vibration, 2011, 330(26):6311-6335 doi: 10.1016/j.jsv.2011.07.039
[67]	Chen X, Shen Z, He Q, et al. Influence of uncertainty and excitation amplitude on the vibration characteristics of rubber isolators. Journal of Sound and Vibration, 2016, 377:216-225 doi: 10.1016/j.jsv.2016.03.034
[68]	Virgin L, Davis R. Vibration isolation using buckled struts. Journal of Sound and Vibration, 2003, 260:965-973 doi: 10.1016/S0022-460X(02)01177-X
[69]	Ledezma-Ramirez D, Ferguson N, Brennan MJ, et al. An experimental nonlinear low dynamic stiffness device for shock isolation. Journal of Sound and Vibration, 2015, 347:1-13 doi: 10.1016/j.jsv.2015.02.006
[70]	Huang X, Chen Y, Hua H, et al. Shock isolation performance of a nonlinear isolator using Euler buckled beam as negative stiffness corrector:Theoretical and experimental study. Journal of Sound and Vibration, 2015, 345:178-196 doi: 10.1016/j.jsv.2015.02.001
[71]	Peng Z, Meng G, Lang Z, et al. Study of the effects on cubic nonlinear damping on vibration isolations using Harmonic Balance Method. International Journal of Non-linear Mechanics, 2012, 47: 1073-1080 doi: 10.1016/j.ijnonlinmec.2011.09.013
[72]	Peng Z, Lang Z, Zhao L, et al. The force transmissibility of MDOF structures with a non-linear viscous damping device. International Journal of Non-Linear Mechanics, 2011, 46:1305-1314 doi: 10.1016/j.ijnonlinmec.2011.06.009
[73]	Guo P, Lang Z, Peng Z. Analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation system. Nonlinear Dynamics, 2012, 67:2671-2687 doi: 10.1007/s11071-011-0180-6
[74]	Laalej H, Lang Z, Daley S, et al. Application of non-linear damping to vibration isolation:an experimental study. Nonlinear Dynamics, 2012, 69:409-421 doi: 10.1007/s11071-011-0274-1
[75]	Lang Z, Jing X, Billings SA, et al. Theoretical study of the effects of nonlinear viscous damping on vibration isolation of sdof systems. Journal of Sound and Vibration, 2009, 323(1):352-365 https://www.researchgate.net/publication/229389973_Theoretical_study_of_the_effects_of_nonlinear_viscous_damping_on_vibration_isolation_of_sdof_systems
[76]	Tang B, Brennan MJ. A comparison of two nonlinear damping mechanisms in a vibration isolator. Journal of Sound and Vibration, 2013, 332(3):510-520 doi: 10.1016/j.jsv.2012.09.010
[77]	Sun J, Huang X, Liu X, et al. Study on the force transmissibility of vibration isolators with geometric nonlinear damping. Nonlinear Dynamics, 2013, 74:1103-1112 doi: 10.1007/s11071-013-1027-0
[78]	Xiao Z, Jing X, Cheng L. The transmissibility of vibration isolators with cubic nonlinear damping under both force and base excitations. Journal of Sound and Vibration, 2013, 332(5):1335-1354 doi: 10.1016/j.jsv.2012.11.001
[79]	Lang Z, Guo P, Takewaki I. Output frequency response function based design of additional nonlinear viscous dampers for vibration control of multi-degree-of-freedom systems. Journal of Sound and Vibration, 2013, 332:4461-4481 doi: 10.1016/j.jsv.2013.04.001
[80]	Peng Z, Lang Z. Effects of anti-symmetric nonlinear viscous damping on the force transmissibility of multi-degree of freedom structures. Theoretical & Applied Mechanics Letters, 2011, 1:063004 https://www.researchgate.net/publication/257961909_Effects_of_anti-symmetric_nonlinear_viscous_damping_on_the_force_transmissibility_of_multi-degree_of_freedom_structures
[81]	Peng Z, Lang Z, Meng G, et al. Reducing force transmissibility in multiple degrees of freedom structures through anti-symmetric nonlinear viscous damping. Acta Mechanica Sinica, 2012, 28(5): 1436-1448 doi: 10.1007/s10409-012-0100-0
[82]	Lü Q, Yao Z. Analysis of the effects of nonlinear viscous damping on vibration isolator. Nonlinear Dynamics, 2015, 79:2325-2332 doi: 10.1007/s11071-014-1814-2
[83]	Huang X, Sun J, Hua H, et al. The isolation performance of vibration systems with general velocity-displacement-dependent nonlinear damping under base excitation:Numerical and experimental study. Nonlinear Dynamics, 2016, 85:77-796 https://www.researchgate.net/publication/298907333_The_isolation_performance_of_vibration_systems_with_general_velocity-displacement-dependent_nonlinear_damping_under_base_excitation_numerical_and_experimental_study
[84]	Lu L, Lin G, Shih M. An experimental study on a generalized Maxwell model for nonlinear viscoelastic dampers used in seismic isolation. Engineering Structures, 2012, 34:111-123 doi: 10.1016/j.engstruct.2011.09.012
[85]	Mokni L, Belhaq M. Using delayed damping to minimize transmitted vibrations. Communications in Nonlinear Science and Numerical Simulation, 2012, 17:1980-1985 doi: 10.1016/j.cnsns.2011.08.034
[86]	Mu T, Zhou L, Yang JN. Comparison of adaptive structural damage identification techniques in nonlinear hysteretic vibration isolation systems. Earthquake Engineering and Engineering Vibration, 2013, 12(4):659-667 doi: 10.1007/s11803-013-0204-y
[87]	Awrejcewicz J, Olejnik P. Stick-slip dynamics of a two-degree-offreedom system. International Journal of Bifurcation and Chaos, 2003, 13(4):843-861 doi: 10.1142/S0218127403006960
[88]	Bhattacharya B. Principles of Vibration Control. New York:Wiely, 2014
[89]	Cveticanin L. On the truly nonlinear oscillator with positive and negative damping. Applied Mathematics and Computation, 2014, 243: 433-445 doi: 10.1016/j.amc.2014.06.009
[90]	Sharma A, Patidar V, Purohit G. Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping. Communications in Nonlinear Science and Numerical Simulation, 2012, 17: 2254-2269 doi: 10.1016/j.cnsns.2011.10.032
[91]	Ho C, Lang Z, Billings S. A frequency domain analysis of the effects of nonlinear damping on the Duffing equation. Mechanical Systems and Signal Processing, 2014, 45(1):49-67 doi: 10.1016/j.ymssp.2013.10.027
[92]	Ho C, Lang Z, Billings S. Design of vibration isolators by exploiting the beneficial effects of stiffness and damping nonlinearities. Journal of Sound and Vibration, 2014, 333(12):2489-2504 doi: 10.1016/j.jsv.2014.02.011
[93]	Huang D, Xu W, Xie W, et al. Dynamical properties of a forced vibration isolation system with real-power nonlinearities in restoring and damping forces. Nonlinear Dynamics, 2015, 81:641-658 doi: 10.1007/s11071-015-2016-2
[94]	汪玉, 陈国均, 华宏星等.船舶动力装置双层隔振系统的优化设计.中国造船, 2001, 42(1):45-49 http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC200101007.htm Wang Yu, Chen Guojun, Hua Hongxing, et al. Optimal design of ship floating raft system power equipment. Ship Building of China, 2001, 42(1):45-49 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZGZC200101007.htm
[95]	Lu Z, Brennan MJ, Yang T, et al. An investigation of a two-stage nonlinear vibration isolation system. Journal of Sound and Vibration, 2013, 332(6):1456-1464 doi: 10.1016/j.jsv.2012.11.019
[96]	Yang K, Harne RL, Wang K, et al. Investigation of a bistable dualstage vibration isolator under harmonic excitation. Smart Materials and Structures, 2014, 23(4):045033 doi: 10.1088/0964-1726/23/4/045033
[97]	Lu Z, Yang T, Brennan MJ, et al. On the performance of a twostage vibration isolation system which has geometrically nonlinear stiffness. ASME Journal of Vibration and Acoustics, 2014, 136(6): 064501 doi: 10.1115/1.4028379
[98]	Wang Y, Li S, Neild SA, et al. Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dynamics, 2017 (in press) https://www.researchgate.net/publication/311895556_Comparison_of_the_dynamic_performance_of_nonlinear_one_and_two_degree-of-freedom_vibration_isolators_with_quasi-zero_stiffness
[99]	Wang X, Zhou J, Xu D, et al. Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dynamics, 2017, 87:633-646 doi: 10.1007/s11071-016-3065-x
[100]	Lu Z, Yang T, Brennan MJ, et al. Experimental investigation of a two-stage nonlinear vibration isolation system with high-static-lowdynamic stiffness. ASME Journal of Applied Mechanics, 2017, 84: 021001-1 https://www.researchgate.net/publication/309294933_Experimental_Investigation_of_a_Two-Stage_Nonlinear_Vibration_Isolation_System_with_High-_Static-Low-Dynamic_Stiffness
[101]	Moon FC. Chaotic and Fractal Dynamics:An introduction for applied scientists and engineers. Weinheim:Wiley-VCH, 2004
[102]	Lou J, Zhu S, He L, et al. Application of chaos method to line spectra reduction. Journal of Sound and Vibration, 2005, 286:645-652 doi: 10.1016/j.jsv.2004.12.018
[103]	Liu S, Yu X, Zhu S. Study on the chaos anti-control technology in nonlinear vibration isolation system. Journal of Sound and Vibration, 2008, 310:855-864 doi: 10.1016/j.jsv.2007.08.006
[104]	Lou J, Zhu S, He L, et al. Experimental chaos in nonlinear vibration isolation system. Chaos Solitons & Fractals, 2009, 40:1367-1375 http://linkinghub.elsevier.com/retrieve/pii/S0960077907007515
[105]	Harvey JrPS, Wiebe R, Gavin HP. On the chaotic response of a nonlinear rolling isolation system. Physica D:Nonlinear Phenomena, 2013, 256-257:36-42 doi: 10.1016/j.physd.2013.04.013
[106]	Farshi B, Assadi A. Development of a chaotic nonlinear tuned mass damper for optimal vibration response. Communication in Nonlinear Science and Numerical Simulation, 2011, 16:4514-4523 doi: 10.1016/j.cnsns.2011.02.011
[107]	Nayfeh, AH. Nonlinear Interactions:Analytical, Computational, and Experimental Methods. Wiley:New York, 1998
[108]	Chen Y, Chen S. Response and transmissibility of nonlinear isolating systems. Journal of Vibration and Shock, 1998, 17:18-22 http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZNGD200503029.htm
[109]	Kawana R, Tokoyoda T, Sato K, et al. Passage through resonance in a three-degree-of-freedom vibration isolation system. Transactions of the Japan Society of Mechanical Engineers, Part C, 2006, 72(7): 2034-2041 https://keio.pure.elsevier.com/en/publications/passage-through-resonance-in-a-three-degree-of-freedom-vibration-
[110]	Lee YS, Vakakis AF, Bergman LA, et al. Passive non-linear targeted energy transfer and its applications to vibration absorption:a review. Journal of Multi-body Dynamics, 2008, 222:77-134 http://www.citeulike.org/article/2955573
[111]	Vakakis AF, Gendelman OV, Bergman LA, et al. Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems. Springer: Netherlands, 2009
[112]	Yang K, Zhang Y, Ding H, et al. The transmissibility of nonlinear energy sink based on nonlinear output frequency-response functions. Communications in Nonlinear Science and Numerical Simulation, 2017, 44:184-192 doi: 10.1016/j.cnsns.2016.08.008
[113]	杨凯, 张业伟, 丁虎等.基于非线性输出频响函数的NES动力学参数设计.振动与冲击, 2016, 35(21):76-80 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201621013.htm Yang Kai, Zhang Yewei, Ding Hu, et al. Parametric design of nonlinear energy sinks based on nonlinear output frequency-response functions. Journal of Vibration and Shock, 2016, 35(21):76-80 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201621013.htm
[114]	Yang K, Zhang Y, Ding H, et al. Nonlinear energy sink for wholespacecraft vibration reduction. ASME Journal of Vibration and Acoustics, 2017, 139(2):021011 doi: 10.1115/1.4035377
[115]	Harris DA. Vibration Isolation Materials//Noise Control Manual. New York:Springer, 1991
[116]	Thenozhi S, Yu W. Advances in modeling and vibration control of building structures. Annual Reviews in Control, 2013, 37(2):346-364 doi: 10.1016/j.arcontrol.2013.09.012
[117]	Rustighi E, Brennan M, Mace B. A shape memory alloy adaptive tuned vibration absorber:Design and implementation. Smart materials and Structures, 2005, 14(1):19 doi: 10.1088/0964-1726/14/1/002
[118]	Bonello P, Brennan MJ, Elliott SJ, et al. Designs for an adaptive tuned vibration absorber with variable shape stiffness element. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Science, 2005, 461(2064):3955-3976 doi: 10.1098/rspa.2005.1547
[119]	Xia M, Sun Q. Thermomechanical responses of nonlinear torsional vibration with NiTi shape memory alloy-alternative stable states and their jumps. Journal of the Mechanics and Physics of Solids, 2016, (in press) http://linkinghub.elsevier.com/retrieve/pii/S002250961630638X
[120]	Damanpack A, Bodaghi M, Aghdam M, et al. On the vibration control capability of shape memory alloy composite beam. Composite Structure, 2014, 110:325-334 doi: 10.1016/j.compstruct.2013.12.002
[121]	Shinozuka M, Chaudhuri SR, Mishra SK. Shape-Menory-Alloy supplemented lead rubber bearing (SMA-LRB) for seismic isolation. Probabilistic Engineering Mechanics, 2015, 41:34-45 doi: 10.1016/j.probengmech.2015.04.004
[122]	Shaw AD, Carrella A. Force displacement curves of a snapping bistable Plate. Nonlinear Dynamics, 2012, 3:191-197 doi: 10.1007%2F978-1-4614-2416-1_14.pdf
[123]	York D, Wang X, Gordaninejad F. A new MR fluid-elastomer vibration isolator. Journal of Intelligent Material Systems and Structures, 2007, 18(12):1221-1225 doi: 10.1177/1045389X07083622
[124]	Liao W, Lai C. Harmonic analysis of a magnetorheological damper for vibration control. Smart Materials and Structures, 2002, 11(2): 288 doi: 10.1088/0964-1726/11/2/312
[125]	Sims N, Peel D, Stanway R, et al. The electrorheological long-stroke damper:A new modelling technique with experimental validation. Journal of Sound and Vibration, 2000, 229(2):207-227 doi: 10.1006/jsvi.1999.2487
[126]	Dutta S, Chakraborty G. Performance analysis of nonlinear vibration isolator with magneto-rheological damper. Journal of Sound and Vibration, 2014, 333:5097-5114 doi: 10.1016/j.jsv.2014.05.028
[127]	Yu H, Sun X, Xu J, et al. The time-delay coupling nonlinear effect in sky-hook control of vibration isolation systems using MagnetoRheological fluid dampers. Journal of Mechanical Science and Technology, 2016, 30(9):4157-4166 doi: 10.1007/s12206-016-0827-9
[128]	Ozbulut OE, Rosche PN, Lin PY, et al. GA-based optimum design of a shape memory alloy device for seismic response mitigation. Smart Material and Structure, 2010, 19:065004 doi: 10.1088/0964-1726/19/6/065004
[129]	Choi E, Nam TH, Oh JT, et al. An isolation bearing for highway bridges using shape memory alloys. Material Science Engineering, 2006, 438-440:1081-1084 doi: 10.1016/j.msea.2006.05.098
[130]	Ozbulut OE, Hurlebaus S, Desroches R. Seismic response control using shape memory alloys:A review. Journal of Intelligent Material System and Stucture, 2011, 22:1531-1549 doi: 10.1177/1045389X11411220
[131]	束立红, 何琳, 王宇飞等.聚氨酯隔振器非线性力学模型与特性研究.振动工程学报, 2010, 23(5):530-536 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201005008.htm Shu Lihong, He Lin, Wang Yufei, et al. Nonlinear mechanical model and character research on polyurethane isolator. Journal of Vibration Engineering, 2010, 23(5):530-536 (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZDGC201005008.htm
[132]	Daynes S, Nall S, Weaver P, et al. Bistable composite flap for an airfoil. Journal of Aircraft, 2010, 47(1):334-338 doi: 10.2514/1.45389
[133]	Daynes S, Weaver P, Trevarthen J. A morphing composite air inlet with multiple stable shapes. Journal of Intelligent Material Systems and Structures, 2011, 22(9):961-973 doi: 10.1177/1045389X11399943
[134]	Schultz MR. A concept for airfoil-like active bistable twisting structures. Journal of Intelligent Material Systems and Structures, 2008, 19(2):157-169 doi: 10.1177/1045389X06073988
[135]	Gatto A, Mattioni F, Friswell M. Experimental investigation of bistable winglets to enhance aircraft wing lift takeoff capability. Journal of Aircraft, 2009, 46(2):647-655 doi: 10.2514/1.39614
[136]	Diaconu CG, Weaver PM, Mattioni F. Concepts for morphing airfoil sections using bi-stable laminated composite structures. ThinWalled Structures, 2008, 46(6):689-701 https://www.researchgate.net/publication/223566521_Concepts_for_morphing_airfoil_sections_using_bi-stable_laminated_composite_structures
[137]	Lachenal X, Daynes S, Weaver PM. Review of morphing concepts and materials for wind turbine blade applications. Wind Energy, 2013, 16(2):283-307 doi: 10.1002/we.v16.2
[138]	Pirrera A, Avitabile D, Weaver P. Bistable plates for morphing structures:a refined analytical approach with high-order polynomials. International Journal of Solids and Structures, 2010, 47(25):3412-3425 https://www.researchgate.net/publication/223240594_Bistable_plates_for_morphing_structures_A_refined_analytical_approach_with_high-order_polynomials
[139]	Potter K, Weaver P, Seman AA, et al. Phenomena in the bifurcation of unsymmetric composite plates. Composites Part A:Applied Science and Manufacturing, 2007, 38(1):100-106 doi: 10.1016/j.compositesa.2006.01.017
[140]	Tawfik S, Tan X, Ozbay S, et al. Anticlastic stability modeling for cross-ply composites. Journal of Composite Materials, 2007, 41(11):1325-1338 doi: 10.1177/0021998306068073
[141]	Diaconu CG, Weaver PM, Arrieta AF. Dynamic analysis of bi-stable composite plates. Journal of Sound and Vibration, 2009, 322(4): 987-1004 https://www.researchgate.net/profile/Paul_Weaver/publication/223527005_Dynamic_analysis_of_bi-stable_composite_plates/links/55b7997108aec0e5f4382b6a.pdf
[142]	Shaw AD, Neild SA, Wagg DJ, et al. A nonlinear spring mechanism incorporating a bistable composite plate for vibration isolation. Journal of Sound and Vibration, 2013, 332(24):6265-6275 doi: 10.1016/j.jsv.2013.07.016