Applied Mathematics and Mechanics >
Improved dynamic anti-resonance vibration isolator based on a Halbach array negative stiffness mechanism
Received date: 2025-09-15
Revised date: 2026-03-23
Online published: 2026-05-06
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 11872242 and 12121002)
Copyright
To concurrently achieve low-frequency vibration absorption and high-frequency vibration isolation in high-static-stiffness applications, this study proposes a hybrid passive vibration isolator that integrates a lever mechanism with a Halbach array negative stiffness mechanism. The lever mechanism reduces the natural frequency by increasing the system’s effective mass and introduces an anti-resonance frequency. Additionally, the negative stiffness amplified by the lever counteracts the positive stiffness, leading to the substantial reduction in the dynamic stiffness with only a small amount of negative stiffness required. Both theoretical and experimental results indicate that the synergistic integration facilitates the broad isolation bandwidth and effective low-frequency absorption while keeping the added mass minimal and the negative stiffness low. The comparative analysis of several magnetic array configurations demonstrates that, when the isolator dimensions and added mass are held constant, the Halbach array configuration reduces both resonance and anti-resonance frequencies while preserving high-frequency transmissibility. The integrated strategy enables the development of a compact and lightweight isolator, providing an effective solution for low-frequency vibration suppression in scenarios where mass and space are limited.
Jialei DENG , Xinhua LONG . Improved dynamic anti-resonance vibration isolator based on a Halbach array negative stiffness mechanism[J]. Applied Mathematics and Mechanics, 2026 , 47(5) : 941 -964 . DOI: 10.1007/s10483-026-3387-9
| [1] | GATTI, G., BRENNAN, M. J., and TANG, B. Some diverse examples of exploiting the beneficial effects of geometric stiffness nonlinearity. Mechanical Systems and Signal Processing, 125, 4–20 (2019) |
| [2] | IBRAHIM, R. A. Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration, 314, 371–452 (2008) |
| [3] | BALAJI, P. S. and KARTHIK SELVAKUMAR, K. Applications of nonlinearity in passive vibration control: a review. Journal of Vibration Engineering and Technologies, 9, 183–213 (2021) |
| [4] | ?ZYAR, C. and YILMAZ, ?. A self-tuning adaptive-passive lever-type vibration isolation system. Journal of Sound and Vibration, 505, 116159 (2021) |
| [5] | YILMAZ, C. and KIKUCHI, N. Analysis and design of passive low-pass filter-type vibration isolators considering stiffness and mass limitations. Journal of Sound and Vibration, 293, 171–195 (2006) |
| [6] | DESJARDINS, R. A. and HOOPER, W. E. Antiresonant rotor isolation for vibration reduction. Journal of the American Helicopter Society, 25, 46–55 (1980) |
| [7] | LIU, N. N., LI, C. Y., YIN, C. Y., DONG, X. J., and HUA, H. X. Application of a dynamic antiresonant vibration isolator to minimize the vibration transmission in underwater vehicles. Journal of Vibration and Control, 24, 3819–3829 (2018) |
| [8] | IVOVICH, V. A. and SAVOVICH, M. K. Isolation of floor machines by lever-type inertial vibration corrector. Proceedings of the Institution of Civil Engineers-Structures and Buildings, 146, 391–402 (2001) |
| [9] | FLANNELLY, W. G. Dynamic Antiresonant Vibration Isolator, US Patent, 3, 322, 379 (1967) |
| [10] | YILMAZ, C. and KIKUCHI, N. Analysis and design of passive band-stop filter-type vibration isolators for low-frequency applications. Journal of Sound and Vibration, 291, 1004–1028 (2006) |
| [11] | YAN, B., WANG, Z. H., MA, H. Y., BAO, H. H., WANG, K., and WU, C. Y. A novel lever-type vibration isolator with eddy current damping. Journal of Sound and Vibration, 494, 115862 (2021) |
| [12] | DENG, J. L., YANG, J. N., JIAO, S. J., and LONG, X. H. Band-stop characteristics of a nonlinear anti-resonant vibration isolator for low-frequency applications. International Journal of Mechanical Sciences, 240, 107914 (2023) |
| [13] | SMITH, M. C. Synthesis of mechanical networks: the inerter. IEEE Transactions on Automatic Control, 47, 1648–1662 (2002) |
| [14] | KUHNERT, W. M., GON?ALVES, P. J. P., LEDEZMA-RAMIREZ, D. F., and BRENNAN, M. J. Inerter-like devices used for vibration isolation: a historical perspective. Journal of the Franklin Institute, 358, 1070–1086 (2021) |
| [15] | LI, Y. H., HU, N. Q., YANG, Y., CHENG, Z., YIN, Z. Y., ZHOU, Z. B., and HU, J. T. Physical realizations of inerter and inerter-based vibration control. Heliyon, 10, e35870 (2024) |
| [16] | LIU, C. N., CHEN, L., LEE, H. P., YANG, Y., and ZHANG, X. L. A review of the inerter and inerter-based vibration isolation: theory, devices, and applications. Journal of the Franklin Institute, 359, 7677–7707 (2022) |
| [17] | WANG, F. C., HONG, M. F., and LIN, T. C. Designing and testing a hydraulic inerter. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225, 66–72 (2011) |
| [18] | JOHN, E. D. A. and WAGG, D. J. Design and testing of a frictionless mechanical inerter device using living-hinges. Journal of the Franklin Institute, 356, 7650–7668 (2019) |
| [19] | DOGAN, H., SIMS, N. D., and WAGG, D. J. Design, testing and analysis of a pivoted-bar inerter device used as a vibration absorber. Mechanical Systems and Signal Processing, 171, 108893 (2022) |
| [20] | SMITH, M. C. and WANG, F. C. Performance benefits in passive vehicle suspensions employing inerters. Vehicle System Dynamics, 42, 235–257 (2004) |
| [21] | MADHAMSHETTY, K. and MANIMALA, J. M. Low-rate characterization of a mechanical inerter. Machines, 6, 32 (2018) |
| [22] | SHEN, Y. J., HUA, J., FAN, W., LIU, Y. L., YANG, X. F., and CHEN, L. Optimal design and dynamic performance analysis of a fractional-order electrical network-based vehicle mechatronic ISD suspension. Mechanical Systems and Signal Processing, 184, 109718 (2023) |
| [23] | WAGG, D. J. A review of the mechanical inerter: historical context, physical realisations and nonlinear applications. Nonlinear Dynamics, 104, 13–34 (2021) |
| [24] | CARRELLA, A., BRENNAN, M. J., WATERS, T. P., and LOPES, V. JR. Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 55, 22–29 (2012) |
| [25] | GATTI, G. An adjustable device to adaptively realise diverse nonlinear force-displacement characteristics. Mechanical Systems and Signal Processing, 180, 109379 (2022) |
| [26] | ZHAO, F., JI, J. C., YE, K., and LUO, Q. T. Increase of quasi-zero stiffness region using two pairs of oblique springs. Mechanical Systems and Signal Processing, 144, 106975 (2020) |
| [27] | GATTI, G. A nonlinear quasi-zero stiffness vibration isolator with quintic restoring force characteristic: a fundamental analytical insight. Journal of Vibration and Control, 30, 4185–4198 (2024) |
| [28] | MENG, Q. Y., HOU, L., LIN, R. Z., CHEN, Y. S., SAEED, N. A., FOULY, A., and AWWAD, E. M. On a quasi-zero stiffness vibration isolator with multiple zero stiffness points for mass load deviation. Applied Mathematical Modelling, 145, 116112 (2025) |
| [29] | 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) |
| [30] | 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) |
| [31] | LIAN, X. Y., LIU, B., DENG, H. X., and GONG, X. L. A vibration isolator with a controllable quasi-zero stiffness region based on nonlinear force design. Applied Mathematics and Mechanics (English Edition), 45(8), 1279–1294 (2024) https://doi.org/10.1007/s10483-024-3137-8 |
| [32] | ZHOU, J. X., WANG, X. L., XU, D. L., 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) |
| [33] | 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) |
| [34] | MAO, X. Y., YIN, M. M., DING, H., GENG, X. F., SHEN, Y. J., and CHEN, L. Q. Modeling, analysis, and simulation of X-shape quasi-zero-stiffness-roller vibration isolators. Applied Mathematics and Mechanics (English Edition), 43(7), 1027–1044 (2022) https://doi.org/10.1007/s10483-022-2871-6 |
| [35] | YAN, B., YU, N., and WU, C. Y. A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms. Applied Mathematics and Mechanics (English Edition), 43(7), 1045–1062 (2022) https://doi.org/10.1007/s10483-022-2868-5 |
| [36] | DONG, G. X., ZHANG, X. N., XIE, S. L., YAN, B., and LUO, Y. J. 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) |
| [37] | YAN, B., YU, N., WANG, Z. H., WU, C. Y., WANG, S., and ZHANG, W. M. Lever-type quasi-zero stiffness vibration isolator with magnetic spring. Journal of Sound and Vibration, 527, 116865 (2022) |
| [38] | WANG, X. J., YU, N., WU, C. Y., ZHANG, W. M., and YAN, B. Lever-type high-static-low-dynamic-stiffness vibration isolator with electromagnetic shunt damping. International Journal of Non-Linear Mechanics, 146, 104128 (2022) |
| [39] | KOCAK, K. and YILMAZ, C. Design of a compliant lever-type passive vibration isolator with quasi-zero-stiffness mechanism. Journal of Sound and Vibration, 558, 117758 (2023) |
| [40] | YUAN, J. J., JIN, G. Y., YE, T. G., BAI, J. L., and SUN, Z. X. Improving quasi-zero-stiffness isolator performance: two hybrid isolators employing inerter elements. Applied Mathematical Modelling, 135, 212–242 (2024) |
| [41] | DENG, J. L., ZHAO, J. H., YANG, J. N., TIAN, Y., and LONG, X. H. Design and analysis of a tunable electromagnetic lever-type anti-resonant vibration isolator. International Journal of Mechanical Sciences, 263, 108787 (2024) |
| [42] | LIU, C. C., JING, X. J., and LI, F. M. Vibration isolation using a hybrid lever-type isolation system with an X-shape supporting structure. International Journal of Mechanical Sciences, 98, 169–177 (2015) |
| [43] | DENG, J. L., YANG, J. N., ZHAO, J. H., and LONG, X. H. An approach for realizing lightweight quasi-zero stiffness isolators via lever amplification. Journal of Sound and Vibration, 596, 118740 (2025) |
| [44] | 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) |
| [45] | WU, J. L., ZENG, L. Z., HAN, B., ZHOU, Y. F., LUO, X., LI, X. Q., CHEN, X. D., and JIANG, W. Analysis and design of a novel arrayed magnetic spring with high negative stiffness for low-frequency vibration isolation. International Journal of Mechanical Sciences, 216, 106980 (2022) |
| [46] | CHEN, Z. S., ZHANG, Y. Y., XIONG, Y. P., and WANG, A. K. Analytical investigations of nonlinear stiffness characteristics of Halbach-cylinder magnetic springs for heavy-load capacity. Applied Sciences, 15, 5099 (2025) |
| [47] | HUANG, Z. X., ZHU, G. N., YANG, T., HU, R. C., and JIANG, B. L. Halbach-array torsional nonlinear vibration isolator and its application to floating-slab track. Nonlinear Dynamics, 113, 24303–24327 (2025) |
| [48] | ZHANG, Y., LIU, Q. H., LEI, Y. G., CAO, J. Y., and LIAO, W. H. Halbach high negative stiffness isolator: modeling and experiments. Mechanical Systems and Signal Processing, 188, 110014 (2023) |
| [49] | ZHANG, Y., LIU, Q. H., LEI, Y. G., CAO, J. Y., and LIAO, W. H. Circular Halbach negative stiffness isolating from torsional vibration: design, modeling and experiments. Mechanical Systems and Signal Processing, 202, 110711 (2023) |
| [50] | ALLAG, H. and YONNET, J. P. 3-D analytical calculation of the torque and force exerted between two cuboidal magnets. IEEE Transactions on Magnetics, 45, 3969–3972 (2009) |
| [51] | ALLAG, H., YONNET, J. P., and LATRECHE, M. E. H. 3D analytical calculation of forces between linear Halbach-type permanent-magnet arrays. 8th International Symposium on Advanced Electromechanical Motion Systems and Electric Drives Joint Symposium, IEEE, France, 1–6 (2009) |
/
| 〈 |
|
〉 |
Email Alert
RSS