Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (7): 1045-1062.doi: https://doi.org/10.1007/s10483-022-2868-5
• Articles • Previous Articles Next Articles
Bo YAN, Ning YU, Chuanyu WU
Received:
2021-10-08
Revised:
2022-01-07
Online:
2022-07-01
Published:
2022-06-30
Contact:
Chuanyu WU, E-mail: cywu@zstu.edu.cn
Supported by:
2010 MSC Number:
Bo YAN, Ning YU, Chuanyu WU. A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms. Applied Mathematics and Mechanics (English Edition), 2022, 43(7): 1045-1062.
[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. 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