[1] LIU, C., JING, X., DALEY, S., and LI, F. Recent advances in micro-vibration isolation. Mechanical Systems and Signal Processing, 56-57, 55-80(2015)
[2] DEN HARTOG, J. P. Mechanical Vibrations, Dover Publications, New York (1985)
[3] YANG, T., ZHOU, S., FANG, S., QIN, W., and INMAN, D. J. Nonlinear vibration energy harvesting and vibration suppression technologies:designs, analysis, and applications. Applied Physics Reviews, 8, 031317(2021)
[4] ALABUZHEV, P. Vibration Protection and Measuring Systems with Quasi-zero Stiffness, CRC Press, Boca Ration (1989)
[5] PLATUS, D. L. Negative-stiffness-mechanism vibration isolation systems, vibration control in microelectronics, optics, and metrology. International Society for Optics and Photonics, 1619, 44-54(1992)
[6] IBRAHIM, R. A. Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 314, 371-452(2008)
[7] CARRELLA, A., BRENNAN, M. J., and WATERS, T. P. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 301, 678-689(2007)
[8] WANG, K., ZHOU, J., CAI, C., XU, D., XIA, S., and WEN, G. Bidirectional deep-subwavelength band gap induced by negative stiffness. Journal of Sound and Vibration, 515, 116474(2021)
[9] KOVACIC, I., BRENNAN, M. J., and WATERS, T. P. A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. Journal of Sound and Vibration, 315, 700-711(2008)
[10] KOVACIC, I., BRENNAN, M. J., and LINETON, B. Effect of a static force on the dynamic behaviour of a harmonically excited quasi-zero stiffness system. Journal of Sound and Vibration, 325, 870-883(2009)
[11] LIU, X., HUANG, X., and HUA, H. On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. Journal of Sound and Vibration, 332, 3359-3376(2013)
[12] HUANG, X., LIU, X., SUN, J., ZHANG, Z., and HUA, H. Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector:a theoretical and experimental study. Journal of Sound and Vibration, 333, 1132-1148(2014)
[13] DING, H. and CHEN, L. Q. Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dynamics, 95, 2367-2382(2019)
[14] ARAKI, Y., ASAI, T., KIMURA, K., MAEZAWA, K., and MASUI, T. Nonlinear vibration isolator with adjustable restoring force. Journal of Sound and Vibration, 332, 6063-6077(2013)
[15] LU, Z., BRENNAN, M. J., YANG, T., LI, X., and LIU, Z. An investigation of a two-stage nonlinear vibration isolation system. Journal of Sound and Vibration, 332, 1456-1464(2013)
[16] ZHOU, J., WANG, X., XU, D., and BISHOP, S. Nonlinear dynamic characteristics of a quasi-zero stiffness vibration isolator with cam-roller-spring mechanisms. Journal of Sound and Vibration, 346, 53-69(2015)
[17] SUN, X., JING, X., XU, J., and CHENG, L. Vibration isolation via a scissor-like structured platform. Journal of Sound and Vibration, 333, 2404-2420(2014)
[18] FENG, X. and JING, X. Human body inspired vibration isolation:beneficial nonlinear stiffness, nonlinear damping&nonlinear inertia. Mechanical Systems and Signal Processing, 117, 786-812(2019)
[19] JING, X., ZHANG, L., FENG, X., SUN, B., and LI, Q. A novel bio-inspired anti-vibration structure for operating hand-held jackhammers. Mechanical Systems and Signal Processing, 118, 317-339(2019)[1] LIU, C., JING, X., DALEY, S., and LI, F. Recent advances in micro-vibration isolation. Mechanical Systems and Signal Processing, 56-57, 55-80(2015)
[2] DEN HARTOG, J. P. Mechanical Vibrations, Dover Publications, New York (1985)
[3] YANG, T., ZHOU, S., FANG, S., QIN, W., and INMAN, D. J. Nonlinear vibration energy harvesting and vibration suppression technologies:designs, analysis, and applications. Applied Physics Reviews, 8, 031317(2021)
[4] ALABUZHEV, P. Vibration Protection and Measuring Systems with Quasi-zero Stiffness, CRC Press, Boca Ration (1989)
[5] PLATUS, D. L. Negative-stiffness-mechanism vibration isolation systems, vibration control in microelectronics, optics, and metrology. International Society for Optics and Photonics, 1619, 44-54(1992)
[6] IBRAHIM, R. A. Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 314, 371-452(2008)
[7] CARRELLA, A., BRENNAN, M. J., and WATERS, T. P. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 301, 678-689(2007)
[8] WANG, K., ZHOU, J., CAI, C., XU, D., XIA, S., and WEN, G. Bidirectional deep-subwavelength band gap induced by negative stiffness. Journal of Sound and Vibration, 515, 116474(2021)
[9] KOVACIC, I., BRENNAN, M. J., and WATERS, T. P. A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. Journal of Sound and Vibration, 315, 700-711(2008)
[10] KOVACIC, I., BRENNAN, M. J., and LINETON, B. Effect of a static force on the dynamic behaviour of a harmonically excited quasi-zero stiffness system. Journal of Sound and Vibration, 325, 870-883(2009)
[11] LIU, X., HUANG, X., and HUA, H. On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. Journal of Sound and Vibration, 332, 3359-3376(2013)
[12] HUANG, X., LIU, X., SUN, J., ZHANG, Z., and HUA, H. Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector:a theoretical and experimental study. Journal of Sound and Vibration, 333, 1132-1148(2014)
[13] DING, H. and CHEN, L. Q. Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dynamics, 95, 2367-2382(2019)
[14] ARAKI, Y., ASAI, T., KIMURA, K., MAEZAWA, K., and MASUI, T. Nonlinear vibration isolator with adjustable restoring force. Journal of Sound and Vibration, 332, 6063-6077(2013)
[15] LU, Z., BRENNAN, M. J., YANG, T., LI, X., and LIU, Z. An investigation of a two-stage nonlinear vibration isolation system. Journal of Sound and Vibration, 332, 1456-1464(2013)
[16] ZHOU, J., WANG, X., XU, D., and BISHOP, S. Nonlinear dynamic characteristics of a quasi-zero stiffness vibration isolator with cam-roller-spring mechanisms. Journal of Sound and Vibration, 346, 53-69(2015)
[17] SUN, X., JING, X., XU, J., and CHENG, L. Vibration isolation via a scissor-like structured platform. Journal of Sound and Vibration, 333, 2404-2420(2014)
[18] FENG, X. and JING, X. Human body inspired vibration isolation:beneficial nonlinear stiffness, nonlinear damping&nonlinear inertia. Mechanical Systems and Signal Processing, 117, 786-812(2019)
[19] JING, X., ZHANG, L., FENG, X., SUN, B., and LI, Q. A novel bio-inspired anti-vibration structure for operating hand-held jackhammers. Mechanical Systems and Signal Processing, 118, 317-339(2019) A state-of-the-art review on low-frequency nonlinear vibration isolation 1059
[20] WANG, Y. and JING, X. Nonlinear stiffness and dynamical response characteristics of an asymmetric X-shaped structure. Mechanical Systems and Signal Processing, 125, 142-169(2019)
[21] BIAN, J. and JING, X. Superior nonlinear passive damping characteristics of the bio-inspired limb-like or X-shaped structure. Mechanical Systems and Signal Processing, 125, 21-51(2019)
[22] DAI, H., CAO, X., JING, X., WANG, X., and YUE, X. Bio-inspired anti-impact manipulator for capturing non-cooperative spacecraft:theory and experiment. Mechanical Systems and Signal Processing, 142, 106785(2020)
[23] DENG, T., WEN, G., DING, H., LU, Z. Q., and CHEN, L. Q. A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck. Mechanical Systems and Signal Processing, 145, 106967(2020)
[24] YAN, G., ZOU, H. X., WANG, S., ZHAO, L. C., GAO, Q. H., TAN, T., and ZHANG, W. M. Large stroke quasi-zero stiffness vibration isolator using three-link mechanism. Journal of Sound and Vibration, 478, 115344(2020)
[25] YAN, G., ZOU, H. X., WANG, S., ZHAO, L. C., WU, Z. Y., and ZHANG, W. M. Bio-inspired toe-like structure for low-frequency vibration isolation. Mechanical Systems and Signal Processing, 162, 108010(2022)
[26] YAN, G., ZOU, H. X., WANG, S., ZHAO, L. C., WU, Z. Y., and ZHANG, W. M. Bio-inspired vibration isolation:methodology and design. Applied Mechanics Reviews, 73, 020801(2021)
[27] YAN, B., MA, H., JIAN, B., WANG, K., and WU, C. Nonlinear dynamics analysis of a bi-state nonlinear vibration isolator with symmetric permanent magnets. Nonlinear Dynamics, 97, 2499-2519(2019)
[28] XU, D., YU, Q., ZHOU, J., and BISHOP, S. R. Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 332, 3377-3389(2013)
[29] ZHENG, Y., ZHANG, X., LUO, Y., YAN, B., and MA, C. Design and experiment of a highstatic-low-dynamic stiffness isolator using a negative stiffness magnetic spring. Journal of Sound and Vibration, 360, 31-52(2016)
[30] YAN, B., MA, H., ZHAO, C., WU, C., WANG, K., and WANG, P. A vari-stiffness nonlinear isolator with magnetic effects:theoretical modeling and experimental verification. International Journal of Mechanical Sciences, 148, 745-755(2018)
[31] CARRELLA, A., BRENNAN, M. J., WATERS, T. P., and SHIN, K. On the design of a high-staticlow-dynamic stiffness isolator using linear mechanical springs and magnets. Journal of Sound and Vibration, 315, 712-720(2008)
[32] YAN, B., MA, H., YU, N., ZHANG, L., and WU, C. Theoretical modeling and experimental analysis of nonlinear electromagnetic shunt damping. Journal of Sound and Vibration, 471, 115184(2020)
[33] KOVACIC, I. and BRENNAN, M. J. The Duffing Equation:Nonlinear Oscillators and Their Behaviour, John Wiley&Sons, New Jersey (2011)
[34] NAYFEH, A. H. and MOOK, D. T. Nonlinear oscillations, John Wiley&Sons, New Jersey (2008)
[35] MOFIDIAN, S. M. M. and BARDAWEEL, H. Displacement transmissibility evaluation of vibration isolation system employing nonlinear-damping and nonlinear-stiffness elements. Journal of Vibration and Control, 24, 4247-4259(2017)
[36] PENG, Z. K., MENG, G., LANG, Z. Q., ZHANG, W. M., and CHU, F. L. Study of the effects of cubic nonlinear damping on vibration isolations using harmonic balance method. International Journal of Non-linear Mechanics, 47, 1073-1080(2012)
[37] FURLANI, E. P. Permanent Magnet and Electromechanical Devices, Academic Press, San Diego (2001)
[38] YAN, B., MA, H., ZHANG, L., ZHENG, W., WANG, K., and WU, C. A bistable vibration isolator with nonlinear electromagnetic shunt damping. Mechanical Systems and Signal Processing, 136, 106504(2020)
[39] ZHOU, S. and ZUO, L. Nonlinear dynamic analysis of asymmetric tristable energy harvesters for enhanced energy harvesting. Communications in Nonlinear Science and Numerical Simulation, 61, 271-284(2018)[1] LIU, C., JING, X., DALEY, S., and LI, F. Recent advances in micro-vibration isolation. Mechanical Systems and Signal Processing, 56-57, 55-80(2015)
[2] DEN HARTOG, J. P. Mechanical Vibrations, Dover Publications, New York (1985)
[3] YANG, T., ZHOU, S., FANG, S., QIN, W., and INMAN, D. J. Nonlinear vibration energy harvesting and vibration suppression technologies:designs, analysis, and applications. Applied Physics Reviews, 8, 031317(2021)
[4] ALABUZHEV, P. Vibration Protection and Measuring Systems with Quasi-zero Stiffness, CRC Press, Boca Ration (1989)
[5] PLATUS, D. L. Negative-stiffness-mechanism vibration isolation systems, vibration control in microelectronics, optics, and metrology. International Society for Optics and Photonics, 1619, 44-54(1992)
[6] IBRAHIM, R. A. Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 314, 371-452(2008)
[7] CARRELLA, A., BRENNAN, M. J., and WATERS, T. P. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 301, 678-689(2007)
[8] WANG, K., ZHOU, J., CAI, C., XU, D., XIA, S., and WEN, G. Bidirectional deep-subwavelength band gap induced by negative stiffness. Journal of Sound and Vibration, 515, 116474(2021)
[9] KOVACIC, I., BRENNAN, M. J., and WATERS, T. P. A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. Journal of Sound and Vibration, 315, 700-711(2008)
[10] KOVACIC, I., BRENNAN, M. J., and LINETON, B. Effect of a static force on the dynamic behaviour of a harmonically excited quasi-zero stiffness system. Journal of Sound and Vibration, 325, 870-883(2009)
[11] LIU, X., HUANG, X., and HUA, H. On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. Journal of Sound and Vibration, 332, 3359-3376(2013)
[12] HUANG, X., LIU, X., SUN, J., ZHANG, Z., and HUA, H. Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector:a theoretical and experimental study. Journal of Sound and Vibration, 333, 1132-1148(2014)
[13] DING, H. and CHEN, L. Q. Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dynamics, 95, 2367-2382(2019)
[14] ARAKI, Y., ASAI, T., KIMURA, K., MAEZAWA, K., and MASUI, T. Nonlinear vibration isolator with adjustable restoring force. Journal of Sound and Vibration, 332, 6063-6077(2013)
[15] LU, Z., BRENNAN, M. J., YANG, T., LI, X., and LIU, Z. An investigation of a two-stage nonlinear vibration isolation system. Journal of Sound and Vibration, 332, 1456-1464(2013)
[16] ZHOU, J., WANG, X., XU, D., and BISHOP, S. Nonlinear dynamic characteristics of a quasi-zero stiffness vibration isolator with cam-roller-spring mechanisms. Journal of Sound and Vibration, 346, 53-69(2015)
[17] SUN, X., JING, X., XU, J., and CHENG, L. Vibration isolation via a scissor-like structured platform. Journal of Sound and Vibration, 333, 2404-2420(2014)
[18] FENG, X. and JING, X. Human body inspired vibration isolation:beneficial nonlinear stiffness, nonlinear damping&nonlinear inertia. Mechanical Systems and Signal Processing, 117, 786-812(2019)
[19] JING, X., ZHANG, L., FENG, X., SUN, B., and LI, Q. A novel bio-inspired anti-vibration structure for operating hand-held jackhammers. Mechanical Systems and Signal Processing, 118, 317-339(2019) A state-of-the-art review on low-frequency nonlinear vibration isolation 1059
[20] WANG, Y. and JING, X. Nonlinear stiffness and dynamical response characteristics of an asymmetric X-shaped structure. Mechanical Systems and Signal Processing, 125, 142-169(2019)
[21] BIAN, J. and JING, X. Superior nonlinear passive damping characteristics of the bio-inspired limb-like or X-shaped structure. Mechanical Systems and Signal Processing, 125, 21-51(2019)
[22] DAI, H., CAO, X., JING, X., WANG, X., and YUE, X. Bio-inspired anti-impact manipulator for capturing non-cooperative spacecraft:theory and experiment. Mechanical Systems and Signal Processing, 142, 106785(2020)
[23] DENG, T., WEN, G., DING, H., LU, Z. Q., and CHEN, L. Q. A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck. Mechanical Systems and Signal Processing, 145, 106967(2020)
[24] YAN, G., ZOU, H. X., WANG, S., ZHAO, L. C., GAO, Q. H., TAN, T., and ZHANG, W. M. Large stroke quasi-zero stiffness vibration isolator using three-link mechanism. Journal of Sound and Vibration, 478, 115344(2020)
[25] YAN, G., ZOU, H. X., WANG, S., ZHAO, L. C., WU, Z. Y., and ZHANG, W. M. Bio-inspired toe-like structure for low-frequency vibration isolation. Mechanical Systems and Signal Processing, 162, 108010(2022)
[26] YAN, G., ZOU, H. X., WANG, S., ZHAO, L. C., WU, Z. Y., and ZHANG, W. M. Bio-inspired vibration isolation:methodology and design. Applied Mechanics Reviews, 73, 020801(2021)
[27] YAN, B., MA, H., JIAN, B., WANG, K., and WU, C. Nonlinear dynamics analysis of a bi-state nonlinear vibration isolator with symmetric permanent magnets. Nonlinear Dynamics, 97, 2499-2519(2019)
[28] XU, D., YU, Q., ZHOU, J., and BISHOP, S. R. Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. Journal of Sound and Vibration, 332, 3377-3389(2013)
[29] ZHENG, Y., ZHANG, X., LUO, Y., YAN, B., and MA, C. Design and experiment of a highstatic-low-dynamic stiffness isolator using a negative stiffness magnetic spring. Journal of Sound and Vibration, 360, 31-52(2016)
[30] YAN, B., MA, H., ZHAO, C., WU, C., WANG, K., and WANG, P. A vari-stiffness nonlinear isolator with magnetic effects:theoretical modeling and experimental verification. International Journal of Mechanical Sciences, 148, 745-755(2018)
[31] CARRELLA, A., BRENNAN, M. J., WATERS, T. P., and SHIN, K. On the design of a high-staticlow-dynamic stiffness isolator using linear mechanical springs and magnets. Journal of Sound and Vibration, 315, 712-720(2008)
[32] YAN, B., MA, H., YU, N., ZHANG, L., and WU, C. Theoretical modeling and experimental analysis of nonlinear electromagnetic shunt damping. Journal of Sound and Vibration, 471, 115184(2020)
[33] KOVACIC, I. and BRENNAN, M. J. The Duffing Equation:Nonlinear Oscillators and Their Behaviour, John Wiley&Sons, New Jersey (2011)
[34] NAYFEH, A. H. and MOOK, D. T. Nonlinear oscillations, John Wiley&Sons, New Jersey (2008)
[35] MOFIDIAN, S. M. M. and BARDAWEEL, H. Displacement transmissibility evaluation of vibration isolation system employing nonlinear-damping and nonlinear-stiffness elements. Journal of Vibration and Control, 24, 4247-4259(2017)
[36] PENG, Z. K., MENG, G., LANG, Z. Q., ZHANG, W. M., and CHU, F. L. Study of the effects of cubic nonlinear damping on vibration isolations using harmonic balance method. International Journal of Non-linear Mechanics, 47, 1073-1080(2012)
[37] FURLANI, E. P. Permanent Magnet and Electromechanical Devices, Academic Press, San Diego (2001)
[38] YAN, B., MA, H., ZHANG, L., ZHENG, W., WANG, K., and WU, C. A bistable vibration isolator with nonlinear electromagnetic shunt damping. Mechanical Systems and Signal Processing, 136, 106504(2020)
[39] ZHOU, S. and ZUO, L. Nonlinear dynamic analysis of asymmetric tristable energy harvesters for enhanced energy harvesting. Communications in Nonlinear Science and Numerical Simulation, 61, 271-284(2018)1060 Bo YAN, Ning YU, and Chuanyu WU
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[44] MCDAID, A. J. and MACE, B. R. A self-tuning electromagnetic vibration absorber with adaptive shunt electronics. Smart Materials and Structures, 22, 105013(2013)
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[48] ROBERTSON, W. S., KIDNER, M. R. F., CAZZOLATO, B. S., and ZANDER, A. C. Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation. Journal of Sound and Vibration, 326, 88-103(2009)
[49] WU, W., CHEN, X., and SHAN, Y. Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness. Journal of Sound and Vibration, 333, 2958-2970(2014)
[50] ZHANG, F., XU, M., SHAO, S., and XIE, S. A new high-static-low-dynamic stiffness vibration isolator based on magnetic negative stiffness mechanism employing variable reluctance stress. Journal of Sound and Vibration, 476, 115322(2020)
[51] SUN, X., WANG, F., and XU, J. Analysis, design and experiment of continuous isolation structure with local quasi-zero-stiffness property by magnetic interaction. International Journal of Nonlinear Mechanics, 116, 289-301(2019)
[52] ZHOU, J., XIAO, Q., XU, D., OUYANG, H., and LI, Y. A novel quasi-zero-stiffness strut and its applications in six-degree-of-freedom vibration isolation platform. Journal of Sound and Vibration, 394, 59-74(2017)
[53] YANG, T., CAO, Q., LI, Q., and QIU, H. A multi-directional multi-stable device:modeling, experiment verification and applications. Mechanical Systems and Signal Processing, 146, 106986(2021)
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[56] ZHENG, Y., LI, Q., YAN, B., LUO, Y., and ZHANG, X. A Stewart isolator with high-staticlow-dynamic stiffness struts based on negative stiffness magnetic springs. Journal of Sound and Vibration, 422, 390-408(2018)
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