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A magnetic nonlinear energy sink with quasi-zero stiffness characteristics

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Abstract

Due to their reliable strong nonlinear characteristics, magnetic forces have been used to design nonlinear energy sinks (NES). However, the linear magnetic force affects the performance of NES. In this paper, a quasi-zero stiffness magnetic nonlinear energy sink (QZS-MNES) is proposed. Negative stiffness is introduced to counteract the linear part of the magnetic force. Based on the magnetic force expression of the permanent magnet, the dynamic equations of the linear oscillator (LO) coupled with the QZS-MNES are established. The dynamic characteristics are analyzed by numerical and approximate analytical solutions. Transient response and steady state response are used to discuss the effect of linear magnetic force on the vibration suppression efficiency. Moreover, the vibration suppression of QZS-MNES is compared with the magnetic nonlinear energy sink (MNES) with linear stiffness and the triple-magnet magnetic suspension dynamic vibration absorber (TMSDVA), respectively. The results show that compared with MNES, the elimination of linear magnetic force can improve the parameter adaptability of NES. Compared with TMSDVA, QZS-MNES not only has a better parameter adaptability, but also has a stronger vibration suppression ability. The parameter adaptability of QZS-MNES is verified by particle swarm optimization (PSO) algorithm. In conclusion, the QZS-MNES proposed in this paper is an effective and highly adaptable vibration control strategy. Furthermore, the necessity of eliminating linear stiffness in NES is illustrated.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Quintana, A., Saunders, B.E., Vasconcellos, R., Abdelkefi, A.: Dynamical responses and analysis of rotor-nacelle systems subjected to aerodynamic and base excitations. Nonlinear Dyn. 112(1), 233–258 (2024). https://doi.org/10.1007/s11071-023-09074-6

    Article  Google Scholar 

  2. Hao, M.Y., Ding, H., Mao, X.Y., Chen, L.Q.: Multi-harmonic resonance of pipes conveying fluid with pulsating flow. J. Sound Vib. 569, 117990 (2024). https://doi.org/10.1016/j.jsv.2023.117990

    Article  Google Scholar 

  3. Cui, W., Zhao, L., Ge, Y., Xu, K.: A generalized van der Pol nonlinear model of vortex-induced vibrations of bridge decks with multistability. Nonlinear Dyn. 112(1), 259–272 (2024). https://doi.org/10.1007/s11071-023-09047-9

    Article  Google Scholar 

  4. Deng, T.-C., Ding, H.: Frequency band preservation: pipe design strategy away from resonance. Acta Mech. Sin. 40(3), 523201 (2023). https://doi.org/10.1007/s10409-023-23201-x

    Article  MathSciNet  Google Scholar 

  5. Jiao, X.L., Zhang, J.X., Li, W.B., Wang, Y.Y., Ma, W.L., Zhao, Y.: Advances in spacecraft micro-vibration suppression methods. Prog. Aerosp. Sci. 138, 100898 (2023). https://doi.org/10.1016/j.paerosci.2023.100898

    Article  Google Scholar 

  6. Saeed, A.S., Nasar, R.A., Al-Shudeifat, M.A.: A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types. Nonlinear Dyn. 111(1), 1–37 (2023). https://doi.org/10.1007/s11071-022-08094-y

    Article  Google Scholar 

  7. Yan, B., Yu, N., Ma, H.Y., Wu, C.Y.: A theory for bistable vibration isolators. Mech. Syst. Signal Process. 167, 108507 (2022). https://doi.org/10.1016/j.ymssp.2021.108507

    Article  Google Scholar 

  8. Bednarek, M., Lewandowski, D., Polczyński, K., Awrejcewicz, J.: On the active damping of vibrations using electromagnetic spring. Mech. Based Des. Struct. Mach. 49(8), 1131–1144 (2021). https://doi.org/10.1080/15397734.2020.1819311

    Article  Google Scholar 

  9. Yan, B., Yu, N., Wu, C.Y.: A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms. Appl. Math. Mech. 43(7), 1045–1062 (2022). https://doi.org/10.1007/s10483-022-2868-5

    Article  Google Scholar 

  10. Lu, Q.F., Wang, P., Liu, C.C.: An analytical and experimental study on adaptive active vibration control of sandwich beam. Int. J. Mech. Sci. 232, 107634 (2022). https://doi.org/10.1016/j.ijmecsci.2022.107634

    Article  Google Scholar 

  11. Picavea, J., Gameros, A., Yang, J., Axinte, D.: Vibration suppression using tuneable flexures acting as vibration absorbers. Int. J. Mech. Sci. 222, 107238 (2022). https://doi.org/10.1016/j.ijmecsci.2022.107238

    Article  Google Scholar 

  12. Chai, Y.Y., Jing, X.J., Chao, X.: X-shaped mechanism based enhanced tunable QZS property for passive vibration isolation. Int. J. Mech. Sci. 218, 107077 (2022). https://doi.org/10.1016/j.ijmecsci.2022.107077

    Article  Google Scholar 

  13. Yamada, K., Asami, T.: Passive vibration suppression using 2-degree-of-freedom vibration absorber consisting of a beam and piezoelectric elements. J. Sound Vib. 532, 116997 (2022). https://doi.org/10.1016/j.jsv.2022.116997

    Article  Google Scholar 

  14. Xing, Z.Y., Yang, X.D.: A combined vibration isolation system with quasi-zero stiffness and dynamic vibration absorber. Int. J. Mech. Sci. 256, 108508 (2023). https://doi.org/10.1016/j.ijmecsci.2023.108508

    Article  Google Scholar 

  15. Mucchielli, P., Gogoi, A., Hazra, B., Pakrashi, V.: A mathematically consistent stochastic simulation of a 3D pendulum tuned mass damper and tuning. Nonlinear Dyn. 109(2), 401–418 (2022). https://doi.org/10.1007/s11071-022-07556-7

    Article  Google Scholar 

  16. Zhao, Z.P., Hu, X.Y., Zhang, R.F., Chen, Q.J.: Analytical optimization of the tuned viscous mass damper under impulsive excitations. Int. J. Mech. Sci. 228, 107472 (2022). https://doi.org/10.1016/j.ijmecsci.2022.107472

    Article  Google Scholar 

  17. Su, X.Y., Kang, H.J., Guo, T.D., Cong, Y.Y.: Internal resonance and energy transfer of a cable-stayed beam with a tuned mass damper. Nonlinear Dyn. 110(1), 131–152 (2022). https://doi.org/10.1007/s11071-022-07644-8

    Article  Google Scholar 

  18. Hu, X.Y., Zhao, Z.P., Yang, K., Liao, W., Chen, Q.J.: Novel triple friction pendulum-tuned liquid damper for the wind-induced vibration control of airport control towers. Thin Wall Struct. 182, 110337 (2023). https://doi.org/10.1016/j.tws.2022.110337

    Article  Google Scholar 

  19. Liu, G., Lei, Z., Law, S.S., Yang, Q.: The nonlinear behavior of prestressed tuned mass damper for vibration control of wind turbine towers. Nonlinear Dyn. 111(12), 10939–10955 (2023). https://doi.org/10.1007/s11071-023-08434-6

    Article  Google Scholar 

  20. Cao, Y.B., Yao, H.L., Dou, J.X., Bai, R.X.: A multi-stable nonlinear energy sink for torsional vibration of the rotor system. Nonlinear Dyn. 110(2), 1253–1278 (2022). https://doi.org/10.1007/s11071-022-07681-3

    Article  Google Scholar 

  21. Ma, X.X., Song, Y.X., Cao, P., Li, J., Zhang, Z.G.: Self-excited vibration suppression of a spline-shafting system using a nonlinear energy sink. Int. J. Mech. Sci. 245, 108105 (2023). https://doi.org/10.1016/j.ijmecsci.2023.108105

    Article  Google Scholar 

  22. Cao, Y.B., Li, Z.P., Dou, J.X., Jia, R.Y., Yao, H.L.: An inerter nonlinear energy sink for torsional vibration suppression of the rotor system. J. Sound Vib. 537, 117184 (2022). https://doi.org/10.1016/j.jsv.2022.117184

    Article  Google Scholar 

  23. Al-Shudeifat, M.A.: Effect of negative stiffness content on the periodic motion of nonlinearly coupled oscillators. J. Comput. Nonlinear Dyn. 16(11), 114501 (2021). https://doi.org/10.1115/1.4052287

    Article  Google Scholar 

  24. Sheng, H., He, M.X., Ding, Q.: Vibration suppression by mistuning acoustic black hole dynamic vibration absorbers. J. Sound Vib. 542, 117370 (2023). https://doi.org/10.1016/j.jsv.2022.117370

    Article  Google Scholar 

  25. Dang, W.H., Wang, Z.H., Chen, L.Q., Yang, T.Z.: A high-efficient nonlinear energy sink with a one-way energy converter. Nonlinear Dyn. 109(4), 2247–2261 (2022). https://doi.org/10.1007/s11071-022-07575-4

    Article  Google Scholar 

  26. Wang, T., Tang, Y., Yang, T.Z., Ma, Z.S., Ding, Q.: Bistable enhanced passive absorber based on integration of nonlinear energy sink with acoustic black hole beam. J. Sound Vib. 544, 117409 (2023). https://doi.org/10.1016/j.jsv.2022.117409

    Article  Google Scholar 

  27. Al-Shudeifat, M.A., Saeed, A.S.: Frequency–energy plot and targeted energy transfer analysis of coupled bistable nonlinear energy sink with linear oscillator. Nonlinear Dyn. 105(4), 2877–2898 (2021). https://doi.org/10.1007/s11071-021-06802-8

    Article  Google Scholar 

  28. Davidson, J., Kalmar-Nagy, T., Habib, G.: Parametric excitation suppression in a floating cylinder via dynamic vibration absorbers: a comparative analysis. Nonlinear Dyn. 110(2), 1081–1108 (2022). https://doi.org/10.1007/s11071-022-07710-1

    Article  Google Scholar 

  29. Dang, W.H., Liu, S.L., Chen, L.Q., Yang, T.Z.: A dual-stage inerter-enhanced nonlinear energy sink. Nonlinear Dyn. 111(7), 6001–6015 (2023). https://doi.org/10.1007/s11071-022-08183-y

    Article  Google Scholar 

  30. Guo, M., Tang, L., Wang, H., Liu, H., Gao, S.: A comparative study on transient vibration suppression of magnetic nonlinear vibration absorbers with different arrangements. Nonlinear Dyn. 111(18), 16729–16776 (2023). https://doi.org/10.1007/s11071-023-08732-z

    Article  Google Scholar 

  31. Wang, Y.F., Kang, H.J., Cong, Y.Y., Guo, T.D., Zhu, W.D.: Vibration suppression of a cable under harmonic excitation by a nonlinear energy sink. Commun. Nonlinear Sci. Numer. Simul. 117, 106988 (2023). https://doi.org/10.1016/j.cnsns.2022.106988

    Article  MathSciNet  Google Scholar 

  32. Ji, J.C., Zhang, N.: Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber. J. Sound Vib. 329(11), 2044–2056 (2010). https://doi.org/10.1016/j.jsv.2009.12.020

    Article  Google Scholar 

  33. Li, X., Ding, H., Chen, L.Q.: Effects of weights on vibration suppression via a nonlinear energy sink under vertical stochastic excitations. Mech. Syst. Signal Process. 173, 109073 (2022). https://doi.org/10.1016/j.ymssp.2022.109073

    Article  Google Scholar 

  34. Ding, H., Shao, Y.F.: NES cell. Appl. Math. Mech. 43(12), 1793–1804 (2022). https://doi.org/10.1007/s10483-022-2934-6

    Article  MathSciNet  Google Scholar 

  35. Chen, H.Y., Mao, X.Y., Ding, H., Chen, L.Q.: Elimination of multimode resonances of composite plate by inertial nonlinear energy sinks. Mech. Syst. Signal Process. 135, 106383 (2020). https://doi.org/10.1016/j.ymssp.2019.106383

    Article  Google Scholar 

  36. Lu, X.L., Liu, Z.P., Lu, Z.: Optimization design and experimental verification of track nonlinear energy sink for vibration control under seismic excitation. Struct. Control. Health Monit. 24(12), e2033 (2017). https://doi.org/10.1002/stc.2033

    Article  Google Scholar 

  37. Al-Shudeifat, M.A.: Highly efficient nonlinear energy sink. Nonlinear Dyn. 76(4), 1905–1920 (2014). https://doi.org/10.1007/s11071-014-1256-x

    Article  MathSciNet  Google Scholar 

  38. Yao, H.L., Wang, Y.W., Xie, L.Q., Wen, B.C.: Bi-stable buckled beam nonlinear energy sink applied to rotor system. Mech. Syst. Signal Process. 138, 106546 (2020). https://doi.org/10.1016/j.ymssp.2019.106546

    Article  Google Scholar 

  39. Zeng, Y.C., Ding, H., Du, R.H., Chen, L.Q.: Micro-amplitude vibration suppression of a bistable nonlinear energy sink constructed by a buckling beam. Nonlinear Dyn. 108(4), 3185–3207 (2022). https://doi.org/10.1007/s11071-022-07378-7

    Article  Google Scholar 

  40. Wang, X., Gene, X.F., Mao, X.Y., Ding, H., Jing, X.J., Chen, L.Q.: Theoretical and experimental analysis of vibration reduction for piecewise linear system by nonlinear energy sink. Mech. Syst. Signal Process. 172, 109001 (2022). https://doi.org/10.1016/j.ymssp.2022.109001

    Article  Google Scholar 

  41. Nucera, F., Vakakis, A.F., McFarland, D.M., Bergman, L.A., Kerschen, G.: Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn. 50(3), 651–677 (2007). https://doi.org/10.1007/s11071-006-9189-7

    Article  Google Scholar 

  42. Lo Feudo, S., Touze, C., Boisson, J., Cumunel, G.: Nonlinear magnetic vibration absorber for passive control of a multi-storey structure. J. Sound Vib. 438, 33–53 (2019). https://doi.org/10.1016/j.jsv.2018.09.007

    Article  Google Scholar 

  43. Li, S.B., Ding, H.: A cellular strategy for enhancing the adaptability of nonlinear energy sinks to strong excitation. Int. J. Dyn. Control (2023). https://doi.org/10.1007/s40435-023-01335-x

    Article  Google Scholar 

  44. Al-Shudeifat, M.A.: Frequency-energy analysis of coupled linear oscillator with unsymmetrical nonlinear energy sink. J. Comput. Nonlinear Dyn. 18(2), 024501 (2023). https://doi.org/10.1115/1.4056359

    Article  Google Scholar 

  45. Yang, T., Dang, W., Chen, L.: Two-dimensional inerter-enhanced nonlinear energy sink. Nonlinear Dyn. 112(1), 379–401 (2024). https://doi.org/10.1007/s11071-023-09056-8

    Article  Google Scholar 

  46. Saeed, A.S., Al-Shudeifat, M.A., Cantwell, W.J., Vakakis, A.F.: Two-dimensional nonlinear energy sink for effective passive seismic mitigation. Commun. Nonlinear Sci. Numer. Simul. 99, 105787 (2021). https://doi.org/10.1016/j.cnsns.2021.105787

    Article  MathSciNet  Google Scholar 

  47. Al-Shudeifat, M.A.: Nonlinear energy sinks with piecewise-linear nonlinearities. J. Comput. Nonlinear Dyn. 14(12), 124501 (2019). https://doi.org/10.1115/1.4045052

    Article  Google Scholar 

  48. Zang, J., Yuan, T.C., Lu, Z.Q., Zhang, Y.W., Ding, H., Chen, L.Q.: A lever-type nonlinear energy sink. J. Sound Vib. 437, 119–134 (2018). https://doi.org/10.1016/j.jsv.2018.08.058

    Article  Google Scholar 

  49. Zang, J., Cao, R.Q., Zhang, Y.W.: Steady-state response of a viscoelastic beam with asymmetric elastic supports coupled to a lever-type nonlinear energy sink. Nonlinear Dyn. 105(2), 1327–1341 (2021). https://doi.org/10.1007/s11071-021-06625-7

    Article  Google Scholar 

  50. Cao, R., Wang, Z., Zang, J., Zhang, Y.: Resonance response of fluid-conveying pipe with asymmetric elastic supports coupled to lever-type nonlinear energy sink. Appl. Math. Mech. Engl. Ed. 43(12), 1873–1886 (2022). https://doi.org/10.1007/s10483-022-2925-8

    Article  MathSciNet  Google Scholar 

  51. Wang, X., Mao, X.Y., Ding, H., Lai, S.K., Chen, L.Q.: Multi-resonance inhibition of a two-degree-of-freedom piecewise system by one nonlinear energy sink. Int. J. Dyn. Control (2023). https://doi.org/10.1007/s40435-023-01337-9

    Article  Google Scholar 

  52. Qian, J.M., Chen, L.C., Sun, J.Q.: Random vibration analysis of vibro-impact systems: RBF neural network method. Int. J. Non Linear Mech. 148, 104261 (2023). https://doi.org/10.1016/j.ijnonlinmec.2022.104261

    Article  Google Scholar 

  53. Al-Shudeifat, M.A.: Asymmetric magnet-based nonlinear energy sink. J. Comput. Nonlinear Dyn. 10(1), 014502 (2015). https://doi.org/10.1115/1.4027462

    Article  Google Scholar 

  54. Benacchio, S., Malher, A., Boisson, J., Touze, C.: Design of a magnetic vibration absorber with tunable stiffnesses. Nonlinear Dyn. 85(2), 893–911 (2016). https://doi.org/10.1007/s11071-016-2731-3

    Article  MathSciNet  Google Scholar 

  55. Geng, X.F., Ding, H., Jing, X.J., Mao, X.Y., Wei, K.X., Chen, L.Q.: Dynamic design of a magnetic-enhanced nonlinear energy sink. Mech. Syst. Signal Process. 185, 109813 (2023). https://doi.org/10.1016/j.ymssp.2022.109813

    Article  Google Scholar 

  56. Chen, X.Y., Leng, Y.G., Fan, S.B., Su, X.K., Sun, S.L., Xu, J.J., et al.: Research on dynamic characteristics of a novel triple-magnet magnetic suspension dynamic vibration absorber. J. Vib. Control (2023). https://doi.org/10.1177/10775463231164440

    Article  Google Scholar 

  57. Chen, Y.Y., Qian, Z.C., Zhao, W., Chang, C.M.: A magnetic bi-stable nonlinear energy sink for structural seismic control. J. Sound Vib. 473, 115233 (2020). https://doi.org/10.1016/j.jsv.2020.115233

    Article  Google Scholar 

  58. Chen, Y.Y., Su, W.T., Tesfamariam, S., Qian, Z.C., Zhao, W., Yang, Z.Y., et al.: Experimental study of magnetic bistable nonlinear energy sink for structural seismic control. Soil Dyn. Earthq. Eng. 164, 107572 (2023). https://doi.org/10.1016/j.soildyn.2022.107572

    Article  Google Scholar 

  59. Dou, J.X., Li, Z.P., Cao, Y.B., Yao, H.L., Bai, R.X.: Magnet based bi-stable nonlinear energy sink for torsional vibration suppression of rotor system. Mech. Syst. Signal Process. 186, 109859 (2023). https://doi.org/10.1016/j.ymssp.2022.109859

    Article  Google Scholar 

  60. Zeng, Y.C., Ding, H.: A tristable nonlinear energy sink. Int. J. Mech. Sci. 238, 107839 (2023). https://doi.org/10.1016/j.ijmecsci.2022.107839

    Article  Google Scholar 

  61. Zhang, A., Sorokin, V., Li, H.: Dynamic analysis of a new autoparametric pendulum absorber under the effects of magnetic forces. J. Sound Vib. 485, 115549 (2020). https://doi.org/10.1016/j.jsv.2020.115549

    Article  Google Scholar 

  62. Pilipchuk, V.N., Polczyński, K., Bednarek, M., Awrejcewicz, J.: Guidance of the resonance energy flow in the mechanism of coupled magnetic pendulums. Mech. Mach. Theory 176, 105019 (2022). https://doi.org/10.1016/j.mechmachtheory.2022.105019

    Article  Google Scholar 

  63. Yu, N., Fei, X.Y., Wu, C.Y., Yan, B.: Modeling and analysis of magnetic spring enhanced lever-type electromagnetic energy harvesters. Appl. Math. Mech. 43(5), 743–760 (2022). https://doi.org/10.1007/s10483-022-2849-9

    Article  MathSciNet  Google Scholar 

  64. Shi, G., Tong, D.K., Xia, Y.S., Jia, S.Y., Chang, J., Li, Q., et al.: A piezoelectric vibration energy harvester for multi-directional and ultra-low frequency waves with magnetic coupling driven by rotating balls. Appl. Energy 310, 118511 (2022). https://doi.org/10.1016/j.apenergy.2021.118511

    Article  Google Scholar 

  65. Shao, N., Chen, Z., Wang, X., Zhang, C.X., Xu, J.W., Xu, X.S., et al.: Modeling and analysis of magnetically coupled piezoelectric dual beam with an annular potential energy function for broadband vibration energy harvesting. Nonlinear Dyn. 111(13), 11911–11937 (2023). https://doi.org/10.1007/s11071-023-08503-w

    Article  Google Scholar 

  66. Liu, H.F., Zhao, L.Y., Chang, Y.L., Shan, G.K., Gao, Y.F.: Parameter optimization of magnetostrictive bistable vibration harvester with displacement amplifier. Int. J. Mech. Sci. 223, 107291 (2022). https://doi.org/10.1016/j.ijmecsci.2022.107291

    Article  Google Scholar 

  67. Yan, B., Yu, N., Wang, Z.H., Wu, C.A.Y., Wang, S., Zhang, W.M.: Lever-type quasi-zero stiffness vibration isolator with magnetic spring. J. Sound Vib. 527, 116865 (2022). https://doi.org/10.1016/j.jsv.2022.116865

    Article  Google Scholar 

  68. Yan, G., Wu, Z.Y., Wei, X.S., Wang, S., Zou, H.X., Zhao, L.C., et al.: Nonlinear compensation method for quasi-zero stiffness vibration isolation. J. Sound Vib. 523, 116743 (2022). https://doi.org/10.1016/j.jsv.2021.116743

    Article  Google Scholar 

  69. Lu, Z.Q., Liu, W.H., Ding, H., Chen, L.Q.: Energy transfer of an axially loaded beam with a parallel-coupled nonlinear vibration isolator. J. Vib. Acoust. 144(5), 051009 (2022). https://doi.org/10.1115/1.4054324

    Article  Google Scholar 

  70. Akoun, G., Yonnet, J.P.: 3D analytical calculation of the forces exerted between two cuboidal magnets. IEEE Trans. Magn. 20(5), 1962–1964 (1984). https://doi.org/10.1109/TMAG.1984.1063554

    Article  Google Scholar 

  71. Geng, X.F., Ding, H., Mao, X.Y., Chen, L.Q.: Nonlinear energy sink with limited vibration amplitude. Mech. Syst. Signal Process. 156, 107625 (2021). https://doi.org/10.1016/j.ymssp.2021.107625

    Article  Google Scholar 

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Acknowledgements

The authors would like to gratefully acknowledge the support of the National Science Fund for Distinguished Young Scholars (Grant No. 12025204).

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Authors and Affiliations

  1. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200444, People’s Republic of China

    Xuan-Chen Liu, Hu Ding & Li-Qun Chen

  2. Shaoxing Institute of Technology, Shanghai University, Shaoxing, 312074, People’s Republic of China

    Hu Ding

  3. Department of Mechanical Engineering, Hunan Institute of Engineering, Xiangtan, 411104, Hunan, People’s Republic of China

    Xiao-Feng Geng & Ke-Xiang Wei

  4. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China

    Siu-Kai Lai

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X-CL: Investigation, Writing—original draft. HD: Conceptualization, Funding acquisition, Writing—review and editing. X-FG: Investigation. K-XW: Writing—review. S-KL: Writing—review and editing. L-QC: Writing—editing.

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Liu, XC., Ding, H., Geng, XF. et al. A magnetic nonlinear energy sink with quasi-zero stiffness characteristics. Nonlinear Dyn 112, 5895–5918 (2024). https://doi.org/10.1007/s11071-024-09379-0

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