Modular reconfigurable quasi-zero-stiffness isolators: design, analysis, and experiment

doi:10.1007/s10483-026-3417-7

摘要/Abstract

Abstract:

Quasi-zero-stiffness (QZS) isolators hold considerable promise for the development of low-frequency broadband vibration isolation platforms, particularly in aerospace, transportation, and civil engineering. However, stringent requirements for integration, lightweight design, reliability, and customization in high-end equipment limit the practical application of conventional QZS isolators. To address this challenge, this paper proposes a novel modular reconfigurable QZS isolator (MRQI) composed of elastic modules and complementary rigid modules, which is lightweight and exhibits programmable QZS characteristics. The elastic modules adopt a multi-section beam configuration with compliant joints to reduce stress concentration. Notably, this modular design not only endows the MRQI with reconfigurable and programmable properties but also simplifies fabrication from a three-dimensional (3D) additive manufacturing process to a two-dimensional (2D) planar process, thereby reducing manufacturing errors caused by spatial structural distribution. The results reveal that the MRQI achieves multi-stage QZS characteristics, enabling decoupled control of the QZS range and loading capacity, while each QZS range covers 80% of its corresponding stroke range. Moreover, the MRQI maintains robust low-frequency isolation performance against variations in excitation amplitude and loading mass under both displacement and force excitation conditions, provided that the displacement remains within the QZS ranges. Compared with linear isolators, the MRQI reduces the starting isolation frequency by more than 84%. Both the static and dynamic tests confirm the accuracy of the theoretical analysis. Overall, this work presents a novel approach for constructing scalable, integrated, lightweight, and customizable QZS structures, offering a promising framework for the practical engineering applications of QZS isolators.

Key words: passive vibration isolation, quasi-zero-stiffness (QZS), discrete assembly, user-defined mechanical properties, multi-section buckling beam

中图分类号:

O322

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(8): 1647-1668.

Kangfan YU, Yunwei CHEN, Chuanyun YU, Jianrun ZHANG, Xi LU, Xiaofei DU, Qidi FU. Modular reconfigurable quasi-zero-stiffness isolators: design, analysis, and experiment[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(8): 1647-1668.

图/表 13

Parameter	q/mm	$L t$ /mm	$a t$ /mm	$t t$ /mm	$L s$ /mm	$a s$ /mm	$t s$ /mm	θ₀/(°)
Elastic module 1	0.6	15	10	0.6	70	6	1.0	34
Elastic module 2	0.4	15	15	0.6	70	10	1.2	34
Elastic module 3	0.6	15	15	0.7	70	15	1.2	34
q: initial deflection; $L t :$ straight beam length; $a t :$ straight beam width; $t t :$ straight beam thickness; $L s :$ curved beam length; $a s :$ curved beam width; $t s :$ curved beam thickness

[1]	ZHOU, K., WEN, L. B., GONG, D., ZHOU, J. S., and CHEN, Y. J. Vibro-acoustic analysis and suppression of corrugated sandwich panel structures with general boundary conditions. Thin-Walled Structures, 212, 113196 (2025)
[2]	CHEN, H. T. and JIANG, B. A review of fault detection and diagnosis for the traction system in high-speed trains. IEEE Transactions on Intelligent Transportation Systems, 21(2), 450–465 (2020)
[3]	LIU, H. Z., YAN, Y. D., CUI, J. W., GENG, Y. Q., SUN, T., LUO, X. C., and ZONG, W. J. Recent advances in design and preparation of micro diamond cutting tools. International Journal of Extreme Manufacturing, 6(6), 062008 (2024)
[4]	BALAJI, P. S. and SELVAKUMAR, K. K. Applications of nonlinearity in passive vibration control: a review. Journal of Vibration Engineering & Technologies, 9(2), 183–213 (2021)
[5]	CHEN, N., YANG, Z. C., ZUO, A., JIANG, P. F., JIN, S. K., and XU, Y. L. Bandgap regulations of longitudinal wave for a nonlinear metastructure isolator with high-static-low-dynamic stiffness. Composite Structures, 327, 117706 (2024)
[6]	ZHAO, F., JI, J. C., YE, K., and LUO, Q. T. An innovative quasi-zero stiffness isolator with three pairs of oblique springs. International Journal of Mechanical Sciences, 192, 106093 (2021)
[7]	LEI, H. W., REN, H., ZHOU, P., GUO, F., and WANG, Y. L. Embedding intelligent excitation adaptability for resonance-suppressed QZS vibration isolation. International Journal of Mechanical Sciences, 307, 110931 (2025)
[8]	ZHOU, C. Y., SONG, Y. Z., SUN, H., HU, X. Y., YANG, L. P., PU, H. Y., and LIU, C. Design and experiment of an integrate 3-DoF adjustable QZS vibration isolation system with high-order stability. Mechanical Systems and Signal Processing, 228, 112483 (2025)
[9]	LIU, S. W., PENG, G. L., LI, Z. X., LI, W. H., and SUN, L. D. Low-frequency vibration isolation via an elastic origami-inspired structure. International Journal of Mechanical Sciences, 260, 108622 (2023)
[10]	CHANG, Y. P., ZHOU, J. X., WANG, K., and XU, D. L. Theoretical and experimental investigations on semi-active quasi-zero-stiffness dynamic vibration absorber. International Journal of Mechanical Sciences, 214, 106892 (2022)
[11]	ZHAO, F., JI, J. C., CAO, S. Q., YE, K., and LUO, Q. T. QZS isolators with multi-pairs of oblique bars for isolating ultralow frequency vibrations. Nonlinear Dynamics, 112(3), 1815–1842 (2024)
[12]	JING, X., ZHU, Z., GUO, Y., and LIU, S. 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)
[13]	ZHU, Z. H. and JING, X. J. Nonlinear inertia and its effect within an X-shaped mechanism. Advances in Applied Nonlinear Dynamics, Vibration, and Control – 2023, Springer, Singapore, 554–569 (2024)
[14]	WANG, S. W., LING, P., YAN, G., MA, H. Y., and YAN, B. Multi-stage quasi-zero stiffness vibration isolation with linear-to-torsion magnetic negative stiffness mechanism for variable load. Mechanical Systems and Signal Processing, 249, 114055 (2026)
[15]	LIU, Y. F., OU, H. F., and HU, L. L. A novel isolator with movable cyclic quasi-zero-stiffness enabling low-frequency vibration suppression under arbitrary loads. Mechanical Systems and Signal Processing, 247, 113924 (2026)
[16]	HAN, H. S., WANG, W. Q., YU, B. H., TANG, L. H., WANG, Y. L., and CAO, D. Q. Integrated design of quasi-zero-stiffness vibration isolators based on bifurcation theory. Aerospace Science and Technology, 146, 108940 (2024)
[17]	WU, Y., GUO, M. X., SOROKIN, V., TANG, L. H., FANG, B., AW, K., and HAN, H. S. Multi-directional nonlinear energy sink with quasi-zero stiffness property inspired by origami. Thin-Walled Structures, 218, 114092 (2026)
[18]	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)
[19]	SHU, Y. Q., WANG, K., CHEN, T. T., PAN, H. B., DENG, Y. P., YIN, H. F., and ZHOU, J. X. A quasi-zero-stiffness metastructure for concurrent low-frequency vibration attenuation and energy harvesting. Thin-Walled Structures, 214, 113371 (2025)
[20]	LIU, Z. Q., LYU, Q. F., LI, D. Y., HUAN, R. H., and HUANG, Z. L. A straight-arch-straight beam tandem quasi-zero stiffness structure. International Journal of Mechanical Sciences, 286, 109818 (2025)
[21]	HOU, S. and WEI, J. Z. A quasi-zero stiffness mechanism with monolithic flexible beams for low-frequency vibration isolation. Mechanical Systems and Signal Processing, 210, 111154 (2024)
[22]	HOU, S., WEI, J. Z., SUI, G. D., and XIE, Z. M. Effects of series sequence on the nonlinear dynamic responses of integrated quasi-zero stiffness isolators. Nonlinear Dynamics, 113(11), 12661–12691 (2025)
[23]	ZHANG, Y. S., HOU, F., LU, Z. Q., DING, H., and CHEN, L. Q. Analytical and experimental study of thermoplastic polyurethane inclined beam isolator with quasi-zero stiffness and fractional derivative damping. Mechanical Systems and Signal Processing, 224, 111962 (2025)
[24]	BANERJEE, P., BALAJI, P. S., and MURUGAN, S. A dual-function compliant metastructure based on quasi-zero-stiffness for combined vibration isolation and vibration energy harvesting. International Journal of Dynamics and Control, 13(4), 135 (2025)
[25]	OU, H. F., ZENG, J., LIN, M. Q., WANG, Y. F., ZENG, Y. J., FANG, X., and HU, L. L. Stair-stepping metamaterial and the derived isolator for all-DOF vibrations with multi-payloads. Engineering Structures, 330, 119890 (2025)
[26]	GILMORE, P., GANDHI, U., and SINGH, R. Effect of disk-to-disk variations on the nonlinear static characteristics and stability regimes of coned disk spring stacks: experimental and computational studies of quasi-zero-stiffness isolators. Mechanical Systems and Signal Processing, 219, 111609 (2024)
[27]	PAN, G. P., JIAO, X. L., LIN, C. M., GUAN, Z. F., WU, J. N., LIU, H. L., ZHAO, H. C., and HUANG, H. High load-bearing quasi-zero stiffness metamaterials for vibration isolation. International Journal of Mechanical Sciences, 293, 110225 (2025)
[28]	YIN, G. H., LI, Y. L., PENG, Y., and YAO, S. Customized inverse design of integrative quasi-zero-stiffness metastructures by data-driven method. Engineering Structures, 340, 120744 (2025)
[29]	MA, C., WU, K., WANG, Y. F., and WANG, Y. S. Customized design of periodic metacushion with quasi-zero-stiffness for low-frequency vibration isolation. International Journal of Solids and Structures, 320, 113518 (2025)
[30]	LIU, W. L., WU, L. L., SUN, J. B., and ZHOU, J. Origami-inspired quasi-zero stiffness metamaterials for low-frequency multi-direction vibration isolation. Applied Physics Letters, 123(8), 084102 (2023)
[32]	JIANG, W., ZHANG, X. G., HAN, D., WANG, L., CHEN, W. Q., XIE, Y. M., and REN, X. Experimental and numerical analysis of a novel assembled auxetic structure with two-stage programmable mechanical properties. Thin-Walled Structures, 185, 110555 (2023)
[33]	GUO, X. Y., XU, Y. M., WANG, X., XU, X., ZHU, N., JI, H. B., YUE, Z. S., LI, Z., JI, Y., LI, B. Y., and WANG, P. F. Hierarchical discrete assembly of mechanical metamaterials with application to modular unmanned aerial systems. Advanced Materials Technologies, 11(3), e01455 (2026)
[34]	ZHA, W. Y., YANG, R., YAO, Y. T., LIU, Y. J., and LENG, J. S. Negative stiffness mechanical metamaterial with controllably programmable bandgaps. International Journal of Mechanical Sciences, 303, 110614 (2025)
[35]	HE, J., LIANG, T. B., WANG, Y. H., XIA, L., and XIONG, Y. Quasi-zero stiffness metamaterials with programmable multistability for multi-scenario applications. Applied Materials Today, 46, 102864 (2025)
[36]	WANG, W. J., ZHANG, W. M., GUO, M. F., YANG, H., and MA, L. Impact resistance of assembled plate-lattice auxetic structures. Composite Structures, 338, 118132 (2024)
[37]	ZHANG, Z. Q., NIU, M. Q., and CHEN, L. Q. Analysis and optimization of a quasi-zero-stiffness vibration isolator based on partially rigidized compliant mechanisms. Engineering Structures, 343, 121048 (2025)
[38]	LIU, C. P. and JING, X. J. X-mechanism guided topological design on quasi-zero stiffness meta-ring. Mechanical Systems and Signal Processing, 234, 112814 (2025)
[39]	CHEN, Y. H., NIU, M. Q., FAN, Y. M., and CHEN, L. Q. Quasi-zero-stiffness vibration isolation via a double-layer compliant mechanism. International Journal of Mechanical Sciences, 304, 110670 (2025)
[40]	LIU, W. F., JANBAZ, S., DYKSTRA, D., ENNIS, B., and COULAIS, C. Harnessing plasticity in sequential metamaterials for ideal shock absorption. Nature, 634(8035), 842–847 (2024)
[41]	YU, K., CHEN, Y., YU, C., LI, P., REN, Z., ZHANG, J., and LU, X. Origami-inspire quasi-zero stiffness structure for flexible low-frequency vibration isolation. International Journal of Mechanical Sciences, 276, 109377 (2024)
[31]	ZHENG, P. Y., HAN, B., LIU, Z. P., WANG, Q. Z., WANG, Z. Y., and ZHANG, Q. Multistable twist metastructures with enhanced collapsibility and multidimensional programmability. Additive Manufacturing, 95, 104550 (2024)
[42]	YU, K., CHEN, Y., YU, C., ZHANG, J., and LU, X. A compact nonlinear stiffness-modulated structure for low-frequency vibration isolation under heavy loads. Nonlinear Dynamics, 112(8), 5863–5893 (2024)