An investigation on self-powered semi-active vibration isolation system with adjustable stiffness

doi:10.1007/s10483-026-3384-6

摘要/Abstract

Abstract:

The semi-active vibration isolator (SAVI) has the characteristics of dynamic adjustable stiffness and damping, which can achieve high-efficient broadband vibration isolation. However, the issue of the energy supply constraints on its application in engineering. A novel self-powered semi-active vibration isolator (SPSAVI) with adjustable stiffness is proposed to achieve vibration reduction and energy harvesting. The piezoelectric materials are adhered onto the buckling beam structure to gather the electrical energy generated by vibration, which can supply the energy demand of the piezoelectric actuator for achieving the self-supply capability. An electromechanical coupling dynamic model of the SPSAVI is established under Newton’s second law. The vibration reduction and self-powered effect of the SPSAVI are analyzed by the harmonic balance method. The results indicate that the SPSAVI can effectively improve the vibration isolation performance and achieve the self-powered effect. When the external excitation is 0.65g in which g is the gravity acceleration, the SPSAVI can achieve a stable self-powered effect.

Key words: semi-active vibration isolator (SAVI), adjustable stiffness, piezoelectric material, vibration reduction, energy harvesting

中图分类号:

O322

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(5): 1019-1040.

Kefan XU, Zhuoda ZHOU, Yaohua LIU, Yewei ZHANG, Liqun CHEN. An investigation on self-powered semi-active vibration isolation system with adjustable stiffness[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(5): 1019-1040.

图/表 18

参考文献 58

[1]	ZHANG, Z. G., YUAN, Z. X., WU, M. K., XIAO, Z. Y., CHEN, X. D., ZENG, L. Z., and LI, X. Q. Design of hybrid controller for broadband vibration isolation with active negative stiffness and ground-hook. Mechanical Systems and Signal Processing, 222, 111773 (2025)
[2]	BA, H., NIU, M. Q., and CHEN, L. Q. An adjustable stiffness vibration isolator implemented by a semicircular ring. Mechanical Systems and Signal Processing, 222, 111797 (2025)
[3]	LI, Y. L., WU, Z. Y., PENG, Y., YAO, S., and ZHOU, J. X. Full-band vibration isolation of multi-step quasi-zero stiffness systems. International Journal of Mechanical Sciences, 274, 109277 (2024)
[4]	DAI, W., XU, W. Y., WANG, L., YANG, J., LI, T. Y., ZHU, X., MENG, X. L., and RAN, L. Y. Synergetic integration of elastic constraint and linkages for enhancing vibration isolation. International Journal of Mechanical Sciences, 296, 110308 (2025)
[5]	BIAN, J. and JING, X. J. A nonlinear X-shaped structure based tuned mass damper with multi-variable optimization (X-absorber). Communications in Nonlinear Science and Numerical Simulation, 99, 105829 (2021)
[6]	YAN, G., LU, J. J., QI, W. H., LIU, F. R., YAN, H., ZHAO, L. C., WU, Z. Y., and ZHANG, W. M. Linear and nonlinear stiffness compensation for low-frequency vibration isolation: a comparative study. Nonlinear Dynamics, 112, 5955–5973 (2024)
[7]	ZHANG, Z., NIU, M. Q., YUAN, K., and ZHANG, Y. W. Research on linear/nonlinear viscous damping and hysteretic damping in nonlinear vibration isolation systems. Applied Mathematics and Mechanics (English Edition), 41(7), 983–998 (2020) https://doi.org/10.1007/s10483-020-2630-6
[8]	SUN, K., TANG, J., WU, Z. J., LI, Y. H., and CAO, D. Q. Coupled nonlinear vibration characteristics of quasi-zero-stiffness Gough-Stewart isolation platform. Aerospace Science and Technology, 152, 109352 (2024)
[9]	XU, K. F., NIU, M. Q., ZHANG, Y. W., and CHEN, L. Q. An active high-static-low-dynamic-stiffness vibration isolator with adjustable buckling beams: theory and experiment. Applied Mathematics and Mechanics (English Edition), 45(3), 425–440 (2024) https://doi.org/10.1007/s10483-024-3087-6
[10]	YAN, B., MA, H. Y., ZHAO, C. X., WU, C. Y., WANG, K., and WANG, P. F. A vari-stiffness nonlinear isolator with magnetic effects: theoretical modeling and experimental verification. International Journal of Mechanical Sciences, 148, 745–755 (2018)
[11]	WANG, K., ZHOU, J. X., CAI, C. Q., XU, D. L., and OUYANG, H. J. Mathematical modeling and analysis of a meta-plate for very low-frequency band gap. Applied Mathematical Modelling, 73, 581–597 (2019)
[12]	ZANG, J., YUAN, T. C., LU, Z. Q., ZHANG, Y. W., DING, H., and CHEN, L. Q. A lever-type nonlinear energy sink. Journal of Sound and Vibration, 437, 119–134 (2018)
[13]	LI, T., SEGUY, S., and BERLIOZ, A. On the dynamics around targeted energy transfer for vibro-impact nonlinear energy sink. Nonlinear Dynamics, 87, 1453–1466 (2017)
[14]	SIAMI, A., KARIMI, H. R., CIGADA, A., ZAPPA, E., and SABBIONI, E. Parameter optimization of an inerter-based isolator for passive vibration control of Michelangelo’s Rondanini Pietà. Mechanical Systems and Signal Processing, 98, 667–683 (2018)
[15]	SHI, H. Z., ZHANG, K., LIU, X. B., LIU, H., PENG, H. J., and DENG, Z. C. Vibration suppression of a meta-structure with hybridization of Kresling origami and waterbomb-based origami. Composite Structures, 334, 117964 (2024)
[16]	YU, Y., LIU, N., TIAN, S. Y., HUANG, K. X., ZHOU, Y. X., ZHANG, H., and LUO, J. K. Enhancing vibration energy dissipation and self-powered sensing in high-rise buildings using origami-inspired triboelectric nanogenerators and buckling-restrained braces. Nano Energy, 128, 109838 (2024)
[17]	JING, X. J., CHAI, Y. Y., CHAO, X., and BIAN, J. In-situ adjustable nonlinear passive stiffness using X-shaped mechanisms. Mechanical Systems and Signal Processing, 170, 108267 (2022)
[18]	JING, X. J., ZHU, Z. H., GUO, Y. Q., and LIU, S. H. Nonlinear inertia and its effect within an X-shaped mechanism, part II: nonlinear influences and experimental validations. Mechanical Systems and Signal Processing, 200, 110591 (2023)
[19]	WANG, J. X. and YAO, G. A 3-DOF frog-inspired quasi-zero stiffness isolator and its vibration control performance. Aerospace Science and Technology, 149, 109163 (2024)
[20]	DAI, H. H., JING, X. J., WANG, Y., YUE, X. K., and YUAN, J. P. Post-capture vibration suppression of spacecraft via a bio-inspired isolation system. Mechanical Systems and Signal Processing, 105, 214–240 (2018)
[21]	LIU, W. L., WU, L. L., ZHANG, J. M., SUN, J. B., and ZHOU, J. Metamaterial springs for low-frequency vibration isolation. Journal of Materiomics, 11, 100884 (2025)
[22]	CHEN, X. Y., JI, Q. X., WEI, J. Z., TAN, H. F., YU, J. X., ZHANG, P. F., LAUDE, V., and KADIC, M. Light-weight shell-lattice metamaterials for mechanical shock absorption. International Journal of Mechanical Sciences, 169, 105288 (2020)
[23]	YAO, Y. H., LI, H. G., LI, Y., and WANG, X. J. Analytical and experimental investigation of a high-static-low-dynamic stiffness isolator with cam-roller-spring mechanism. International Journal of Mechanical Sciences, 186, 105888 (2020)
[24]	FAN, H. G., YANG, L. J., TIAN, Y. C., and WANG, Z. W. Design of metastructures with quasi-zero dynamic stiffness for vibration isolation. Composite Structures, 243, 112244 (2020)
[25]	WANG, X. J., LIU, H., CHEN, Y. Q., and GAO, P. Beneficial stiffness design of a high-static-low-dynamic-stiffness vibration isolator based on static and dynamic analysis. International Journal of Mechanical Sciences, 142-143, 235–244 (2018)
[26]	YANG, J. H. and YANG, X. D. Theoretical and experimental study of a novel nonlinear quasi-zero stiffness vibration isolator based on a symmetric link-rod-type structure. Engineering Structures, 301, 117284 (2024)
[27]	ZHANG, F., XU, M. L., SHAO, S. B., and XIE, S. L. 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)
[28]	ZHANG, Y., SHENG, C., HU, Q., LI, M., GUO, Z. X., and QI, R. Dynamic analysis and control application of vibration isolation system with magnetic suspension on satellites. Aerospace Science and Technology, 75, 99–114 (2018)
[29]	LIU, C. R., ZHAO, R., YU, K. P., LEE, H. P., and LIAO, B. P. A quasi-zero-stiffness device capable of vibration isolation and energy harvesting using piezoelectric buckled beams. Energy, 233, 121146 (2021)
[30]	SUI, G. D., ZHOU, C. Y., CHEN, Y. F., ZHANG, X. F., HOU, C. W., SHAN, X. B., and CAO, J. Research on flexible beam-type nonlinear vibration isolators suitable for low frequencies. Ocean Engineering, 293, 116652 (2024)
[31]	HAO, R. B., LU, Z. Q., DING, H., and CHEN, L. Q. Shock isolation of an orthogonal six-DOFs platform with high-static-low-dynamic stiffness. Journal of Applied Mechanics, 90, 111004 (2023)
[32]	GATTI, G. Optimizing elastic potential energy via geometric nonlinear stiffness. Communications in Nonlinear Science and Numerical Simulation, 103, 106035 (2021)
[33]	LIU, X. T., HUANG, X. C., and HUA, H. X. 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)
[34]	FULCHER, B. A., SHAHAN, D. W., HABERMAN, M. R., CONNER SEEPERSAD, C., and WILSON, P. S. Analytical and experimental investigation of buckled beams as negative stiffness elements for passive vibration and shock isolation systems. Journal of Vibration and Acoustics, 136, 031009 (2014)
[35]	HUANG, X. C., LIU, X. T., SUN, J. Y., ZHANG, Z. Y., and HUA, H. X. 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)
[36]	DALELA, S., PRASAD P., BALAJI, P. S., TRIVEDI, S., and KALAM, A. A novel bottom reinforced cosine beam based metastructure with quasi zero stiffness characteristics for vibration isolation applications. Structures, 67, 106950 (2024)
[37]	DALELA, S., BALAJI, P. S., and JENA, D. P. Design of a metastructure for vibration isolation with quasi-zero-stiffness characteristics using bistable curved beam. Nonlinear Dynamics, 108, 1931–1971 (2022)
[38]	SONG, H. N., SHAN, X. B., HOU, W. J., WANG, C., SUN, K. W., and XIE, T. A novel piezoelectric-based active-passive vibration isolator for low-frequency vibration system and experimental analysis of vibration isolation performance. Energy, 278, 127870 (2023)
[39]	QI, R., GE, Y. N., WANG, L., XUE, J. M., YUAN, L. S., SHEN, Z. Y., and JIN, J. M. Electromechanical-coupling modeling and experimental validation of piezoelectric active vibration isolation for truss structures. Mechanical Systems and Signal Processing, 224, 112178 (2025)
[40]	CHEN, R. Z., LI, X. P., YANG, Z. M., XU, J. C., and YANG, H. X. A variable positive-negative stiffness joint with low frequency vibration isolation performance. Measurement, 185, 110046 (2021)
[41]	CHURCHILL, C. B., SHAHAN, D. W., SMITH, S. P., KEEFE, A. C., and MCKNIGHT, G. P. Dynamically variable negative stiffness structures. Science Advances, 2, e1500778 (2016)
[42]	MA, Z. Z., ZHOU, R. P., YANG, Q. C., LEE, H. P., and CHAI, K. A semi-active electromagnetic quasi-zero-stiffness vibration isolator. International Journal of Mechanical Sciences, 252, 108357 (2023)
[43]	MEI, X. T., ZHOU, S. X., YANG, Z. C., KAIZUKA, T., and NAKANO, K. Enhancing energy harvesting in low-frequency rotational motion by a quad-stable energy harvester with time-varying potential wells. Mechanical Systems and Signal Processing, 148, 107167 (2021)
[44]	MA, X. Q., MA, H., and ZHOU, S. X. Nonlinear analysis and response identification of tristable energy harvesters under wind and base excitations. International Journal of Non-Linear Mechanics, 173, 105052 (2025)
[45]	SHI, D. H., CHEN, L., WANG, R. C., JIANG, H. B., and SHEN, Y. J. Design and experiment study of a semi-active energy-regenerative suspension system. Smart Materials and Structures, 24, 015001 (2015)
[46]	FAN, Y. M., ZHANG, Y. K., NIU, M. Q., and CHEN, L. Q. An internal resonance piezoelectric energy harvester based on geometrical nonlinearities. Mechanical Systems and Signal Processing, 211, 111176 (2024)
[47]	JIN, Y. and YANG, T. Z. Enhanced vibration suppression and energy harvesting in fluid-conveying pipes. Applied Mathematics and Mechanics (English Edition), 44(9), 1487–1496 (2023) https://doi.org/10.1007/s10483-023-3022-8
[48]	DU, Y., DENG, J. L., LI, P., and WEN, Y. M. Energy transfer and redistribution: an approach for unifying vibrational energy harvesting and vibration attenuation. Nano Energy, 78, 105245 (2020)
[49]	LI, J. Y. and ZHU, S. Y. Self-powered active vibration control: concept, modeling, and testing. Engineering, 11, 126–137 (2022)
[50]	GAO, X., JIANG, Q. Y., ZHANG, G. C., NIU, J. C., DONG, R. C., and HE, L. Adaptive optimal fault-tolerant vibration control and sensitivity analysis of semi-active suspension based on a self-powered magneto-rheological damper. Smart Materials and Structures, 33, 035030 (2024)
[51]	GAO, X., NIU, J. C., LIU, Z. H., and SHEN, G. D. Influence characteristics of electrical parameters and vibration isolation properties of the stretcher system based on parallel mechanism and self-powered magneto-rheological damper. Journal of Vibration and Control, 26, 552–564 (2020)
[52]	YANG, T., XIE, J. H., HUANG, Z. X., LIU, J. Y., LUO, H. C., and JING, X. J. Bio-inspired vibration isolator with triboelectric nanogenerator for self-powered monitoring. Mechanical Systems and Signal Processing, 223, 111854 (2025)
[53]	YANG, J., CHRISTIE, M. D., SUN, S., NING, D., NAKANO, M., LI, Z., DU, H., and LI, W. H. Integration of an omnidirectional self-powering component to an MRE isolator towards a smart passive isolation system. Mechanical Systems and Signal Processing, 144, 106853 (2020)
[54]	SHI, X., YU, Q. Y., WU, Z. W., LI, J. Y., and ZHU, S. Y. Active control for vehicle suspension using a self-powered dual-function active electromagnetic damper. Journal of Sound and Vibration, 569, 117976 (2024)
[55]	LU, Z. Q., HAO, R. B., WU, D., DING, H., and CHEN, L. Q. An investigation of a self-powered low-frequency nonlinear vibration isolation system. Engineering Structures, 315, 118395 (2024)
[56]	LIANG, F., CHEN, Z. Q., and XU, W. H. Vibration isolation of a self-powered piezoelectric pipe conveying fluid composed of laminated fiber-reinforced composites. Applied Ocean Research, 138, 103664 (2023)
[57]	VIRGIN, L. N. and DAVIS, R. B. Vibration isolation using buckled struts. Journal of Sound and Vibration, 260, 965–973 (2003)
[58]	ERTURK, A. and INMAN, D. J. Issues in mathematical modeling of piezoelectric energy harvesters. Smart Materials and Structures, 17, 065016 (2008)