Applied Mathematics and Mechanics >
An origami-inspired nonlinear energy sink: design, modeling, and analysis
Received date: 2024-12-06
Revised date: 2025-02-11
Online published: 2025-04-07
Supported by
Project supported by the National Science Fund for Distinguished Young Scholars (No. 12025204) and the China Scholarship Council (No. 202206890066)
Copyright
Designing, modeling, and analyzing novel nonlinear elastic elements for the nonlinear energy sink (NES) have long been an attractive research topic. Since gravity is difficult to overcome, previous NES research mainly focused on horizontal vibration suppression. This study proposes an origami-inspired NES. A stacked Miura-origami (SMO) structure, consisting of two Miura-ori sheets, is adopted to construct a nonlinear elastic element. By adjusting the initial angle and the connecting crease torsional stiffness, the quasi-zero stiffness (QZS) and load-bearing capacity can be customized to match the corresponding mass, establishing the vertical SMO-NES. The dynamic model of the SMO-NES coupled with a linear oscillator (LO) is derived for vibrations in the vertical direction. The approximate analytical solutions of the dynamic equation are obtained by the harmonic balance method (HBM), and the solutions are verified numerically. The parameter design principle of the SMO-NES is provided. Finally, the vibration reduction performance of the SMO-NES is studied. The results show that the proposed SMO-NES can overcome gravity and achieve quasi-zero nonlinear restoring force. Therefore, the SMO-NES has the ability of wide-frequency vibration reduction, and can effectively suppress vertical vibrations. By adjusting the initial angle and connecting the crease torsional stiffness of the SMO, the SMO-NES can be achieved with different loading weights, effectively suppressing the vibrations with different primary system masses and excitation amplitudes. In conclusion, with the help of popular origami structures, this study proposes a novel NES, and starts the research of combining origami and NES.
Youcheng ZENG, Hu DING, J. C. JI . An origami-inspired nonlinear energy sink: design, modeling, and analysis[J]. Applied Mathematics and Mechanics, 2025 , 46(4) : 601 -616 . DOI: 10.1007/s10483-025-3239-6
| [1] | CHILLEMI, M., FURTMüLLER, T., ADAM, C., and PIRROTTA, A. Fluid inerter-based vibration control of multi-modal structures subjected to vertical vibration. Engineering Structures, 307, 117938 (2024) |
| [2] | LIU, C. C., JING, X. J., DALEY, S., and LI, F. M. Recent advances in micro-vibration isolation. Mechanical Systems and Signal Processing, 56-57, 55–80 (2015) |
| [3] | GUZMAN PUJOLS, J. C. and RYAN, K. L. Computational simulation of slab vibration and horizontal-vertical coupling in a full-scale test bed subjected to 3D shaking at E-Defense. Earthquake Engineering & Structural Dynamics, 47(2), 438–459 (2017) |
| [4] | TOWARD, M. G. R. and GRIFFIN, M. J. The transmission of vertical vibration through seats: influence of the characteristics of the human body. Journal of Sound and Vibration, 330(26), 6526–6543 (2011) |
| [5] | ZHU, Y. N., GUO, X. Y., WANG, Q., and CAO, D. X. A lightweight tuned particle damper for low-frequency vibration attenuation. Journal of Sound and Vibration, 583, 118440 (2024) |
| [6] | ABé, M. and FUJINO, Y. Dynamic characterization of multiple tuned mass dampers and some design formulas. Earthquake Engineering & Structural Dynamics, 23(8), 813–835 (2007) |
| [7] | ZHANG, Y. F., KONG, X. R., YUE, C. F., and GUO, J. S. Characteristic analysis and design of nonlinear energy sink with cubic damping considering frequency detuning. Nonlinear Dynamics, 111(17), 15817–15836 (2023) |
| [8] | VAKAKIS, A. F., MANEVITCH, L. I., GENDELMAN, O., and BERGMAN, L. Dynamics of linear discrete systems connected to local, essentially non-linear attachments. Journal of Sound and Vibration, 264(3), 559–577 (2003) |
| [9] | LI, M., LI, S. B., and DING, H. Analysis of damping efficiency of nonlinear energy sink cell(in Chinese). Chinese Journal of Theoretical and Applied Mechanics, 55(11), 2614–2623 (2023) |
| [10] | CAO, Y. B., YAO, H. L., HAN, J. C., LI, Z. A., and WEN, B. C. Application of non-smooth NES in vibration suppression of rotor-blade systems. Applied Mathematical Modelling, 87, 351–371 (2020) |
| [11] | GAO, Q. Y. and YANG, T. Z. A nonlinear vibration isolator with an essentially nonlinear converter. Applied Mathematical Modelling, 136, 115648 (2024) |
| [12] | LI, W. K., WANG, Z. M., BRENNAN, M. J., and YANG, T. J. Design and optimization of a two-degrees-of-freedom single-sided vibro-impact nonlinear energy sink for transient vibration suppression of a thin plate. Journal of Sound and Vibration, 587, 118512 (2024) |
| [13] | LIAO, X., CHEN, L., ZHOU, S., and ZHANG, M. L. A novel vari-potential bistable nonlinear energy sink for improved vibration suppression: numerical and experimental study. Nonlinear Dynamics, 111(21), 19763–19790 (2023) |
| [14] | DOU, J. X., YAO, H. L., LI, H., LI, J. L., and JIA, R. Y. A track nonlinear energy sink with restricted motion for rotor systems. International Journal of Mechanical Sciences, 259, 108631 (2023) |
| [15] | LI, S. B., ZHOU, X. X., and CHEN, J. E. Hamiltonian dynamics and targeted energy transfer of a grounded bistable nonlinear energy sink. Communications in Nonlinear Science and Numerical Simulation, 117, 106898 (2023) |
| [16] | MA, K., DU, J. T., LIU, Y., and CHEN, X. M. Torsional vibration attenuation of a closed-loop engine crankshaft system via the tuned mass damper and nonlinear energy sink under multiple operating conditions. Mechanical Systems and Signal Processing, 207, 110941 (2024) |
| [17] | DING, H. and CHEN, L. Q. Designs, analysis, and applications of nonlinear energy sinks. Nonlinear Dynamics, 100(4), 3061–3107 (2020) |
| [18] | WANG, J. J. and ZHENG, Y. Q. Development and robustness investigation of track-based asymmetric nonlinear energy sink for impulsive response mitigation. Engineering Structures, 286, 116127 (2023) |
| [19] | WANG, Y., WANG, P. L., MENG, H. D., and CHEN, L. Q. Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink. Applied Mathematics and Mechanics (English Edition), 45(1), 85–110 (2023) http://doi.org/10.1007/s10483-024-3070-7 |
| [20] | WANG, Y., ZHANG, T., YIN, Y., and WEI, X. H. Reducing shimmy oscillation of a dual-wheel nose landing gear based on torsional nonlinear energy sink. Nonlinear Dynamics, 112(6), 4027–4062 (2024) |
| [21] | DOU, J. X., YAO, H. L., CAO, Y. B., HAN, S. D., and BAI, R. X. Enhancement of bistable nonlinear energy sink based on particle damper. Journal of Sound and Vibration, 547, 117547 (2023) |
| [22] | YAO, H. L., CAO, Y. B., ZHANG, S. J., and WEN, B. C. A novel energy sink with piecewise linear stiffness. Nonlinear Dynamics, 94(3), 2265–2275 (2018) |
| [23] | ZHANG, S. T., ZHOU, J. X., DING, H., and WANG, K. Micro-vibration mitigation of a cantilever beam by one-third power nonlinear energy sinks. Aerospace Science and Technology, 153, 109409 (2024) |
| [24] | DING, H. and SHAO, Y. F. NES cell. Applied Mathematics and Mechanics (English Edition), 43(12), 1793–1804 (2022) https://doi.org/10.1007/s10483-022-2934-6 |
| [25] | RONCEN, T., MICHON, G., and MANET, V. Design and experimental analysis of a pneumatic nonlinear energy sink. Mechanical Systems and Signal Processing, 190, 110088 (2023) |
| [26] | AL-SHUDEIFAT, M. A. Highly efficient nonlinear energy sink. Nonlinear Dynamics, 76(4), 1905–1920 (2014) |
| [27] | CHEN, J. E., SUN, M., HU, W. H., ZHANG, J. H., and WEI, Z. C. Performance of non-smooth nonlinear energy sink with descending stiffness. Nonlinear Dynamics, 100(1), 255–267 (2020) |
| [28] | WANG, J. J., ZHENG, Y. Q., MA, Y. H., and WANG, B. Experimental study on asymmetric and bistable nonlinear energy sinks enabled by side tracks. Mechanical Systems and Signal Processing, 206, 110874 (2024) |
| [29] | ZENG, Y. C., DING, H., JI, J. C., and CHEN, L. Q. Theoretical and experimental study of a stable state adjustable nonlinear energy sink. Mechanical Systems and Signal Processing, 216, 111470 (2024) |
| [30] | GENG, X. F., DING, H., JING, X. J., MAO, X. Y., WEI, K. X., and CHEN, L. Q. Dynamic design of a magnetic-enhanced nonlinear energy sink. Mechanical Systems and Signal Processing, 185, 109813 (2023) |
| [31] | KREMER, D. and LIU, K. F. A nonlinear energy sink with an energy harvester: harmonically forced responses. Journal of Sound and Vibration, 410, 287–302 (2017) |
| [32] | AL-SHUDEIFAT, M. A., WIERSCHEM, N. E., BERGMAN, L. A., and VAKAKIS, A. F. Numerical and experimental investigations of a rotating nonlinear energy sink. Meccanica, 52(4-5), 763–779 (2016) |
| [33] | SAEED, A. S., NASAR, R. A., and AL-SHUDEIFAT, M. A. A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types. Nonlinear Dynamics, 111(1), 1–37 (2022) |
| [34] | CHEN, L. Q., LI, X., LU, Z. Q., ZHANG, Y. W., and DING, H. Dynamic effects of weights on vibration reduction by a nonlinear energy sink moving vertically. Journal of Sound and Vibration, 451, 99–119 (2019) |
| [35] | LI, X., DING, H., and CHEN, L. Q. Effects of weights on vibration suppression via a nonlinear energy sink under vertical stochastic excitations. Mechanical Systems and Signal Processing, 173, 109073 (2022) |
| [36] | LIU, S. W., PENG, G. L., and JIN, K. Towards accurate modeling of the Tachi-Miura origami in vibration isolation platform with geometric nonlinear stiffness and damping. Applied Mathematical Modelling, 103, 674–695 (2022) |
| [37] | FANG, H. B., CHANG, T. S., and WANG, K. W. Magneto-origami structures: engineering multi-stability and dynamics via magnetic-elastic coupling. Smart Materials and Structures, 29(1), 015026 (2020) |
| [38] | JI, J. C., LUO, Q. T., and YE, K. Vibration control based metamaterials and origami structures: a state-of-the-art review. Mechanical Systems and Signal Processing, 161, 107945 (2021) |
| [39] | YU, K. F., CHEN, Y. W., YU, C. Y., LI, P., REN, Z. H., ZHANG, J. R., and LU, X. Origami-inspire quasi-zero stiffness structure for flexible low-frequency vibration isolation. International Journal of Mechanical Sciences, 276, 109377 (2024) |
| [40] | 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) |
| [41] | YE, K. and JI, J. C. Dynamic analysis of the effects of self-weight induced structural and damping nonlinearity on the performance of an origami-inspired vibration isolator. Journal of Sound and Vibration, 547, 117538 (2023) |
| [42] | YE, K., JI, J. C., and FITCH, R. Further investigation and experimental study of an origami structure-based quasi-zero-stiffness vibration isolator. International Journal of Non-Linear Mechanics, 157, 104554 (2023) |
| [43] | 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) |
| [44] | SUN, X. T., LV, Q., QIAN, J. W., and XU, J. Vibration isolation platform for large-amplitude-low-frequency excitation by parallel-stack-assembly design of Miura origamis. International Journal of Non-Linear Mechanics, 166, 104831 (2024) |
/
| 〈 |
|
〉 |
Email Alert
RSS