Abstract
An easily stackable multi-layer quasi-zero-stiffness (ML-QZS) meta-structure is proposed to achieve highly efficient vibration isolation performance at low frequency. First, the distributed shape optimization method is used to design the unit cel, i.e., the single-layer QZS (SL-QZS) meta-structure. Second, the stiffness feature of the unit cell is investigated and verified through static experiments. Third, the unit cells are stacked one by one along the direction of vibration isolation, and thus the ML-QZS meta-structure is constructed. Fourth, the dynamic modeling of the ML-QZS vibration isolation meta-structure is conducted, and the dynamic responses are obtained from the equations of motion, and verified by finite element (FE) simulations. Finally, a prototype of the ML-QZS vibration isolation meta-structure is fabricated by additive manufacturing, and the vibration isolation performance is evaluated experimentally. The results show that the vibration isolation performance substantially enhances when the number of unit cells increases. More importantly, the ML-QZS meta-structure can be easily extended in the direction of vibration isolation when the unit cells are properly stacked. Hence, the ML-FQZS vibration isolation meta-structure should be a fascinating solution for highly efficient vibration isolation performance at low frequency.
Article PDF
Avoid common mistakes on your manuscript.
References
MATICHARD, F., LANTZ, B., MASON, K., MITTLEMAN, R., ABBOTT, B., ABBOTT, S., ALLWINE, E., BARNUM, S., BIRCH, J., BISCANS, S., CLARK, D., COYNE, D., DEBRA, D., DEROSA, R., FOLEY, S., FRITSCHEL, P., GIAIME, J. A., GRAY, C., GRABEEL, G., HANSON, J., HILLARD, M., KISSEL, J., KUCHARCZYK, C., LE ROUX, A., LHUILLIER, V., MACINNIS, M., O’REILLY, B., OTTAWAY, D., PARIS, H., PUMA, M., RADKINS, H., RAMET, C., ROBINSON, M., RUET, L., SAREEN, P., SHOEMAKER, D., STEIN, A., THOMAS, J., VARGAS, M., and WARNER, J. Advanced LIGO two-stage twelve-axis vibration isolation and positioning platform, part 1: design and production overview. Precision Engineering, 40, 273–286 (2015)
JU, L. and BLAIR, D. Compound pendulum test mass systems for laser interferometer gravitational wave detectors. Measurement Science and Technology, 5(9), 1053 (1994)
WEAVER, W., JR, TIMOSHENKO, S. P., and YOUNG, D. H. Vibration Problems in Engineering, John Wiley & Sons, New York (1991)
ALABUZHEV, P. Vibration Protection and Measuring Systems with Quasi-Zero Stiffness, CRC Press, Oxford (1989)
SUN, X., XU, J., and FU, J. The effect and design of time delay in feedback control for a nonlinear isolation system. Mechanical Systems and Signal Processing, 87, 206–217 (2017)
DING, H. and CHEN, L. Q. Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dynamics, 95(3), 2367–2382 (2019)
WANG, K., ZHOU, J., CHANG, Y., OUYANG, H., XU, D., and YANG, Y. A nonlinear ultra-low-frequency vibration isolator with dual quasi-zero-stiffness mechanism. Nonlinear Dynamics, 101, 755–773 (2020)
CARRELLA, A. Passive Vibration Isolators with High-Static-Low-Dynamic-Stiffness, Ph. D. dissertation, University of Southampton, Southampton (2008)
CARRELLA, A., BRENNAN, M. J., WATERS, T. P., and LOPES, V. Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 55(1), 22–29 (2012)
CAO, Q., WIERCIGROCH, M., PAVLOVSKAIA, E. E., GREBOGI, C. T., and THOMPSON, J. M. Archetypal oscillator for smooth and discontinuous dynamics. Physical Review E, 74(4), 046218 (2006)
XU, J. and SUN, X. A multi-directional vibration isolator based on quasi-zero-stiffness structure and time-delayed active control. International Journal of Mechanical Sciences, 100, 126–135 (2015)
LIU, C., TANG, J., YU, K., LIAO, B., HU, R., and ZANG, X. On the characteristics of a quasi-zero-stiffness vibration isolator with viscoelastic damper. Applied Mathematical Modelling, 88, 367–381 (2020)
LIU, C., ZHAO, R., YU, K., and LIAO, B. In-plane quasi-zero-stiffness vibration isolator using magnetic interaction and cables: theoretical and experimental study. Applied Mathematical Modelling, 96, 497–522 (2021)
ZHANG, Q., GUO, D., and HU, G. Tailored mechanical metamaterials with programmable quasi-zero-stiffness features for full-band vibration isolation. Advanced Functional Materials, 31(33), 2101428 (2021)
GATTI, G. Statics and dynamics of a nonlinear oscillator with quasi-zero stiffness behaviour for large deflections. Communications in Nonlinear Science and Numerical Simulation, 83, 105143 (2020)
WEN, G., HE, J., LIU, J., and LIN, Y. Design, analysis and semi-active control of a quasi-zero stiffness vibration isolation system with six oblique springs. Nonlinear Dynamics, 106(1), 309–321 (2021)
CHANG, Y., ZHOU, J., WANG, K., and XU, D. A quasi-zero-stiffness dynamic vibration absorber. Journal of Sound and Vibration, 494, 115859 (2021)
ZHAO, F., JI, J., LUO, Q., CAO, S., CHEN, L., and DU, W. An improved quasi-zero stiffness isolator with two pairs of oblique springs to increase isolation frequency band. Nonlinear Dynamics, 104(1), 349–365 (2021)
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)
YE, K., JI, J. C., and BROWN, T. A novel integrated quasi-zero stiffness vibration isolator for coupled translational and rotational vibrations. Mechanical Systems and Signal Processing, 149, 107340 (2021)
LI, M., CHENG, W., and XIE, R. A quasi-zero-stiffness vibration isolator using a cam mechanism with user-defined profile. International Journal of Mechanical Sciences, 189, 105938 (2021)
SHAN, Y., WU, W., and CHEN, X. Design of a miniaturized pneumatic vibration isolator with high-static-low-dynamic stiffness. Journal of Vibration and Acoustics, 137(4), 045001 (2015)
ZHOU, N. and LIU, K. A tunable high-static-low-dynamic stiffness vibration isolator. Journal of Sound and Vibration, 329(9), 1254–1273 (2010)
ZHENG, Y., ZHANG, X., LUO, Y., ZHANG, Y., and XIE, S. Analytical study of a quasi-zero stiffness coupling using a torsion magnetic spring with negative stiffness. Mechanical Systems and Signal Processing, 100, 135–151 (2018)
YUAN, S., SUN, Y., ZHAO, J., MENG, K., WANG, M., PU, H., PENG, Y., LUO, J., and XIE, S. A tunable quasi-zero stiffness isolator based on a linear electromagnetic spring. Journal of Sound and Vibration, 482, 115449 (2020)
DONG, G., ZHANG, X., XIE, S., YAN, B., and LUO, Y. Simulated and experimental studies on a high-static-low-dynamic stiffness isolator using magnetic negative stiffness spring. Mechanical Systems and Signal Processing, 86, 188–203 (2017)
WANG, Q., ZHOU, J., WANG, K., XU, D., and WEN, G. Design and experimental study of a compact quasi-zero-stiffness isolator using wave springs. Science China Technological Sciences, 64(10), 2255–2271 (2021)
HUANG, X., LIU, X., SUN, J., ZHANG, Z., and HUA, H. Effect of the system imperfections on the dynamic response of a high-static-low-dynamic stiffness vibration isolator. Nonlinear Dynamics, 76(2), 1157–1167 (2014)
SHAW, A. D., NEILD, S. A., WAGG, D. J., WEAVER, P. M., and CARRELLA, A. A nonlinear spring mechanism incorporating a bistable composite plate for vibration isolation. Journal of Sound and Vibration, 332(24), 6265–6275 (2013)
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)
GATTI, G., SHAW, A. D., GONÇALVES, P. J. P., and BRENNAN, M. J. On the detailed design of a quasi-zero stiffness device to assist in the realisation of a translational Lanchester damper. Mechanical Systems and Signal Processing, 164, 108258 (2022)
ZOU, W., CHENG, C., MA, R., HU, Y., and WANG, W. Performance analysis of a quasi-zero stiffness vibration isolation system with scissor-like structures. Archive of Applied Mechanics, 91(1), 117–133 (2020)
SUN, X., JING, X., XU, J., and CHENG, L. Vibration isolation via a scissor-like structured platform. Journal of Sound and Vibration, 333(9), 2404–2420 (2014)
BIAN, J. and JING, X. Analysis and design of a novel and compact X-structured vibration isolation mount (X-mount) with wider quasi-zero-stiffness range. Nonlinear Dynamics, 101(4), 2195–2222 (2020)
ZHAO, F., JI, J., YE, K., and LUO, Q. An innovative quasi-zero stiffness isolator with three pairs of oblique springs. International Journal of Mechanical Sciences, 192, 106093 (2021)
YAN, G., WANG, S., ZOU, H., ZHAO, L., GAO, Q., and ZHANG, W. Bio-inspired polygonal skeleton structure for vibration isolation: design, modelling, and experiment. Science China Technological Sciences, 63(12), 2617–2630 (2020)
ZENG, R., WEN, G., ZHOU, J., and ZHAO, G. Limb-inspired bionic quasi-zero stiffness vibration isolator. Acta Mechanica Sinica, 37(7), 1152–1167 (2021)
SADEGHI, S. and LI, S. Fluidic origami cellular structure with asymmetric quasi-zero stiffness for low-frequency vibration isolation. Smart Materials and Structures, 28(6), 065006 (2019)
HAN, H., SOROKIN, V., TANG, L., and CAO, D. A nonlinear vibration isolator with quasi-zero-stiffness inspired by Miura-origami tube. Nonlinear Dynamics, 105(2), 1313–1325 (2021)
YE, K. and JI, J. C. An origami inspired quasi-zero stiffness vibration isolator using a novel truss-spring based stack Miura-ori structure. Mechanical Systems and Signal Processing, 165, 108383 (2022)
JI, J. C., LUO, Q., and YE, K. Vibration control based metamaterials and origami structures: a state-of-the-art review. Mechanical Systems and Signal Processing, 161, 107945 (2021)
LAN, C. C., WANG, J. H., and CHEN, Y. H. A compliant constant-force mechanism for adaptive robot end-effector operations. IEEE International Conference on Robotics and Automation, 2131–2136 (2010)
GUO, L., KHIU, A., FAN, R. L., and WANG, X. Analysis of a passive scissor-like structure isolator with quasi-zero stiffness for a seating system vibration-isolation application. International Journal of Vehicle Design, 82(1–4), 224–240 (2020)
SUMAN, S., BALAJI, P., SELVAKUMAR, K., and KUMARASWAMIDHAS, L. Nonlinear vibration control device for a vehicle suspension using negative stiffness mechanism. Journal of Vibration Engineering & Technologies, 9(5), 957–966 (2021)
WANG, Y., LI, S., CHENG, C., and SU, Y. Adaptive control of a vehicle-seat-human coupled model using quasi-zero-stiffness vibration isolator as seat suspension. Journal of Mechanical Science and Technology, 32(7), 2973–2985 (2018)
GUO, L., WANG, X., FAN, R. L., and BI, F. Review on development of high-static-low-dynamic-stiffness seat cushion mattress for vibration control of seating suspension system. Applied Sciences, 10(8), 2887 (2020)
ZHU, G., LIU, J., CAO, Q., CHENG, Y., LU, Z., and ZHU, Z. A two degree of freedom stable quasi-zero stiffness prototype and its applications in aseismic engineering. Science China Technological Sciences, 63(3), 496–505 (2020)
WANG, Q., ZHOU, J., XU, D., and OUYANG, H. Design and experimental investigation of ultra-low frequency vibration isolation during neonatal transport. Mechanical Systems and Signal Processing, 139, 106633 (2020)
DING, H., LU, Z. Q., and CHEN, L. Q. Nonlinear isolation of transverse vibration of pre-pressure beams. Journal of Sound and Vibration, 442, 738–751 (2019)
TUO, J., DENG, Z., ZHANG, H., and QIU, J. A 3-axis torsion quasi-zero-stiffness-based sensor system for angular vibration measurement. Journal of Vibration and Control, 24(18), 4325–4336 (2017)
WANG, Y., LI, S., NEILD, S. A., and JIANG, J. Z. Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dynamics, 88(1), 635–654 (2016)
WANG, X., ZHOU, J., XU, D., OUYANG, H., and DUAN, Y. Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dynamics, 87(1), 633–646 (2016)
LU, Z. Q., YANG, T., BRENNAN, M. J., LIU, Z., and CHEN, L. Q. Experimental investigation of a two-stage nonlinear vibration isolation system with high-static-low-dynamic stiffness. Journal of Applied Mechanics, 84(2), 021001 (2017)
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)
SUN, X., QI, Z., and XU, J. A novel multi-layer isolation structure for transverse stabilization inspired by neck structure. Acta Mechanica Sinica, 38(6), 521543 (2022)
LAN, C. C. and LEE, K. M. Generalized shooting method for analyzing compliant mechanisms with curved members. Journal of Mechanical Design, 4, 765–775 (2006)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest The authors declare no conflict of interest.
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 12122206 and 12272129), the Natural Science Foundation of Hunan Province of China (No. 2024JJ4004), and the Zhejiang Provincial Natural Science Foundation of China (No. LQ24A020006)
Rights and permissions
Open access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Zhou, J., Zhou, J., Pan, H. et al. Multi-layer quasi-zero-stiffness meta-structure for high-efficiency vibration isolation at low frequency. Appl. Math. Mech.-Engl. Ed. 45, 1189–1208 (2024). https://doi.org/10.1007/s10483-024-3157-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-024-3157-6