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Nonlinear vibration isolation via a compliant mechanism and wire ropes

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Abstract

Nonlinear vibration isolation systems with both stiffness and damping nonlinearities are promising for a broad-band and high-efficient isolation performance. In this research, a novel nonlinear isolator is proposed via a compliant mechanism with negative stiffness and wire ropes with hysteretic damping. The compliant mechanism consists of two pairs of tilted flexure beams, and the nonlinear restoring force is modelled based on a beam constraint model. The hysteretic restoring force of the wire ropes is characterized by a Bouc–Wen model. A dynamic model of the nonlinear isolator is established, and a semi-analytical method is adopted to analyze the model. Generalized equivalent stiffness and a generalized equivalent damping ratio are defined, respectively, for dynamic systems with multiple nonlinearities. The compliant mechanism exhibits negative stiffness in a limited stroke and endows the isolator with a lower resonant frequency and a smaller resonant amplitude. The complaint mechanism with a symmetric restoring force is more preferred for a broader band of vibration isolation and fewer harmonics in the responses. The wire ropes improve the high-frequency isolation efficiency at the cost of a higher resonant frequency. The incorporation of the compliant mechanism and the wire ropes is beneficial for vibration isolation. Furthermore, the influences of the dimensions of the complaint mechanism on the negative-stiffness stroke, load capacity and vibration isolation performances of the nonlinear isolator are revealed.

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Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Lu, Z.Q., Gu, D.H., Ding, H., Lacarbonara, W., Chen, L.Q.: Nonlinear vibration isolation via a circular ring. Mech. Syst. Signal Process. 136, 106490 (2020)

    Article  Google Scholar 

  2. Ding, H., Chen, L.Q.: Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dyn. 95(3), 2367–2382 (2019)

    Article  MATH  Google Scholar 

  3. Zhang, Y.W., Lu, Y.N., Zhang, W., Teng, Y.Y., Yang, H.X., Yang, T.Z., Chen, L.Q.: Nonlinear energy sink with inerter. Mech. Syst. Signal Process. 125, 52–64 (2019)

    Article  Google Scholar 

  4. Hu, F., Jing, X.: A 6-DOF passive vibration isolator based on Stewart structure with X-shaped legs. Nonlinear Dyn. 91(1), 157–185 (2018)

    Article  Google Scholar 

  5. Shen, Y., Peng, H., Li, X., Yang, S.: Analytically optimal parameters of dynamic vibration absorber with negative stiffness. Mech. Syst. Signal Process. 85, 193–203 (2017)

    Article  Google Scholar 

  6. Li, H., Li, Y., Li, J.: Negative stiffness devices for vibration isolation applications: a review. Adv. Struct. Eng. 23(8), 1739–1755 (2020)

    Article  Google Scholar 

  7. Carrella, A., Brennan, M.J., Kovacic, I., Waters, T.P.: On the force transmissibility of a vibration isolator with quasi-zero-stiffness. J. Sound Vib. 322(4–5), 707–717 (2009)

    Article  Google Scholar 

  8. Wang, X., Liu, H., Chen, Y., Gao, P.: Beneficial stiffness design of a high-static-low-dynamic-stiffness vibration isolator based on static and dynamic analysis. Int. J. Mech. Sci. 142–143, 235–244 (2018)

    Article  Google Scholar 

  9. Lu, Z., Brennan, M.J., Chen, L.Q.: On the transmissibilities of nonlinear vibration isolation system. J. Sound Vib. 375, 28–37 (2016)

    Article  Google Scholar 

  10. Wang, Y., Li, S., Neild, S.A., Jiang, J.Z.: Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dyn. 88(1), 635–654 (2017)

    Article  Google Scholar 

  11. Gatti, G.: Statics and dynamics of a nonlinear oscillator with quasi-zero stiffness behaviour for large deflections. Commun. Nonlinear Sci. Numer. Simul. 83, 105143 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, X., Huang, X., Hua, H.: On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. J. Sound Vib. 332(14), 3359–3376 (2013)

    Article  Google Scholar 

  13. Fulcher B. A., Shahan D. W., Haberman M. R., Seepersad C. C., Wilson P. S.. Analytical and experimental investigation of buckled beams as negative stiffness elements for passive vibration and shock isolation systems. J. Vib. Acoust.; 136(3): 031009.

  14. Huang, X., Liu, X., Sun, J., Zhang, Z., Hua, H.: Vibration isolation characteristics of a nonlinear isolator using euler buckled beam as negative stiffness corrector: a theoretical and experimental study. J. Sound Vib. 333(4), 1132–1148 (2014)

    Article  Google Scholar 

  15. Niu, F., Meng, L., Wu, W., Sun, J., Zhang, W., Meng, G., Rao, Z.: Design and analysis of a quasi-zero stiffness isolator using a slotted conical disk spring as negative stiffness structure. J. Vibroeng. 16(4), 1769–1785 (2014)

    Google Scholar 

  16. Yan, L., Xuan, S., Gong, X.: Shock isolation performance of a geometric anti-spring isolator. J. Sound Vib. 413(443), 120–143 (2018)

    Article  Google Scholar 

  17. Cheng, C., Li, S., Wang, Y., Jiang, X.: On the analysis of a high-static-low-dynamic stiffness vibration isolator with time-delayed cubic displacement feedback. J. Sound Vib. 378, 76–91 (2016)

    Article  Google Scholar 

  18. Zhou, J., Xiao, Q., Xu, D., Ouyang, H., Li, Y.: A novel quasi-zero-stiffness strut and its applications in six-degree-of-freedom vibration isolation platform. J. Sound Vib. 394, 59–74 (2017)

    Article  Google Scholar 

  19. Shi, X., Zhu, S.: Simulation and optimization of magnetic negative stiffness dampers. Sens. Actuators, A 259, 14–33 (2017)

    Article  Google Scholar 

  20. Wang, K., Zhou, J., Ouyang, H., Cheng, L., Xu, D.: A semi-active metamaterial beam with electromagnetic quasi-zero-stiffness resonators for ultralow-frequency band gap tuning. Int. J. Mech. Sci. 176, UNSP105548 (2020)

    Article  Google Scholar 

  21. Howell, L.L., Magleby, S.P., Olsen, B.M.: Handbook of Compliant Mechanisms. Wiley, West Sussex, UK (2013)

    Book  Google Scholar 

  22. Gatti, G.: A K-shaped spring configuration to boost elastic potential energy. Smart Mater. Struct. 28, 077002 (2019)

    Article  Google Scholar 

  23. Xu, Q.: Design of a large-stroke bistable mechanism for the application in constant-force micropositioning stage. J. Mech. Robot. 9(1), 011006 (2016)

    Article  Google Scholar 

  24. Han, Q., Huang, X., Shao, X.: Nonlinear kinetostatic modeling of double-tensural fully-compliant bistable mechanisms. Int. J. Non-Linear Mech. 93, 41–46 (2017)

    Article  Google Scholar 

  25. Zhao, H., Zhao, C., Ren, S., Bi, S.: Analysis and evaluation of a near-zero stiffness rotational flexural pivot. Mech. Mach. Theory 135, 115–129 (2019)

    Article  Google Scholar 

  26. Chen, G., Ma, F., Hao, G., Zhu, W.: Modeling large deflections of initially curved beams in compliant mechanisms using chained beam constraint model. J. Mech. Robot. 11(1), 011002 (2019)

    Article  Google Scholar 

  27. Bai, R., Awtar, S., Chen, G.: A closed-form model for nonlinear spatial deflections of rectangular beams in intermediate range. Int. J. Mech. Sci. 160, 229–240 (2019)

    Article  Google Scholar 

  28. Gao, R., Li, M., Wang, Q., Zhao, J., Liu, S.: A novel design method of bistable structures with required snap-through properties. Sens. Actuators, A 272, 295–300 (2018)

    Article  Google Scholar 

  29. Zhao, J., Zhang, J., Wang, K.W., Cheng, K., Wang, H., Huang, Y., Liu, P.: On the nonlinear snap-through of arch-shaped clamped–clamped bistable beams. J. Appl. Mech. 87(2), 1–5 (2020)

    Article  Google Scholar 

  30. Hao, G.: A framework of designing compliant mechanisms with nonlinear stiffness characteristics. Microsyst. Technol. 24(4), 1795–1802 (2018)

    Article  Google Scholar 

  31. Chen, Q., Zhang, X., Zhang, H., Zhu, B., Chen, B.: Topology optimization of bistable mechanisms with maximized differences between switching forces in forward and backward direction. Mech. Mach. Theory 139, 131–143 (2019)

    Article  Google Scholar 

  32. Lu, Z.Q., Brennan, M., Ding, H., Chen, L.Q.: High-static-low-dynamic-stiffness vibration isolation enhanced by damping nonlinearity. Sci. China Technol. Sci. 62(7), 1103–1110 (2019)

    Article  Google Scholar 

  33. Kiani, M., Amiri, J.V.: Effects of hysteretic damping on the seismic performance of tuned mass dampers. Struct. Design Tall Spec. Build. 28(1), 1555 (2019)

    Article  Google Scholar 

  34. Moradpour, S., Dehestani, M.: Optimal DDBD procedure for designing steel structures with nonlinear fluid viscous dampers. Structures 22, 154–174 (2019)

    Article  Google Scholar 

  35. Wang, G., Wang, Y., Yuan, J., Yang, Y., Wang, D.: Modeling and experimental investigation of a novel arc-surfaced frictional damper. J. Sound Vib. 389, 89–100 (2017)

    Article  Google Scholar 

  36. Barbieri, N., Barbieri, R., Silva, R.A., Mannala, M.J., Barbieri, L.S.V.: Nonlinear dynamic analysis of wire-rope isolator and Stockbridge damper. Nonlinear Dyn. 86(1), 501–512 (2016)

    Article  Google Scholar 

  37. Gerges, R.R., Vickery, B.J.: Design of tuned mass dampers incorporating wire rope springs: Part I: dynamic representation of wire rope springs. Eng. Struct. 27(5), 653–661 (2005)

    Article  Google Scholar 

  38. Carpineto, N., Lacarbonara, W., Vestroni, F.: Hysteretic tuned mass dampers for structural vibration mitigation. J. Sound Vib. 333(5), 1302–1318 (2014)

    Article  Google Scholar 

  39. Carboni, B., Lacarbonara, W., Auricchio, F.: Hysteresis of multiconfiguration assemblies of nitinol and steel strands: experiments and phenomenological identification. J. Eng. Mech. 141(3), 04014135 (2015)

    Google Scholar 

  40. Carboni, B., Lacarbonara, W., Brewick, P.T., Masri, S.F.: Dynamical response identification of a class of nonlinear hysteretic systems. J. Intell. Mater. Syst. Struct. 29(13), 2795–2810 (2018)

    Article  Google Scholar 

  41. Leblouba, M., Rahman, M.E., Barakat, S.: Behavior of polycal wire rope isolators subjected to large lateral deformations. Eng. Struct. 191, 117–128 (2019)

    Article  Google Scholar 

  42. Zhang, Y., Xu, K., Zang, J., Ni, Z., Zhu, Y., Chen, L.: Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions. Appl. Math. Mech. 40(12), 1791–1804 (2019)

    Article  MathSciNet  Google Scholar 

  43. Zheng, L.H., Zhang, Y.W., Ding, H., Chen, L.Q.: Nonlinear vibration suppression of composite laminated beam embedded with NiTiNOL-steel wire ropes. Nonlinear Dyn. 103, 2391–2407 (2021)

    Article  Google Scholar 

  44. Awtar, S., Sen, S.: A generalized constraint model for two-dimensional beam flexures: nonlinear load-displacement formulation. J. Mech. Design 132(8), 081008 (2010)

    Article  Google Scholar 

  45. Casini, P., Vestroni, F.: Nonlinear resonances of hysteretic oscillators. Acta Mech. 229(2), 939–952 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  46. Niu, M.Q., Chen, L.Q.: Dynamic effect of constant inertial acceleration on vibration isolation system with high-order stiffness and Bouc–Wen hysteresis. Nonlinear Dyn. 103, 2227–2240 (2021)

    Article  Google Scholar 

  47. Yuan, T.C., Yang, J., Chen, L.Q.: A harmonic balance approach with alternating frequency/time domain progress for piezoelectric mechanical systems. Mech. Syst. Signal Process. 120, 274–289 (2019)

    Article  Google Scholar 

  48. Wong C. W., Ni Y. Q., Lau S. L. (1994) Steady-state oscillation of hysteretic differential model. I: response analysis. J. Eng. Mech.; 120(11): 2271–2298.

    Google Scholar 

  49. Lacarbonara, W.: Nonlinear Structural Mechanics-Theory, Dynamic Phenomena and Modeling. Springer, New York (2013)

    Book  MATH  Google Scholar 

  50. Huang, J.L., Su, R.K.L., Chen, S.H.: Precise Hsu’s method for analyzing the stability of periodic solutions of multi-degrees-of-freedom systems with cubic nonlinearity. Comput. Struct. 87(23–24), 1624–1630 (2009)

    Article  Google Scholar 

  51. Malatkar, P., Nayfeh, A.H.: Steady-state dynamics of a linear structure weakly coupled to an essentially nonlinear oscillator. Nonlinear Dyn. 47, 167–179 (2007)

    Article  MATH  Google Scholar 

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Acknowledgements

The work is supported by the National Natural Science Foundation of China [11902097, 11872159].

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  1. School of Science, Harbin Institute of Technology, Shenzhen, 518055, China

    Mu-Qing Niu & Li-Qun Chen

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  1. Mu-Qing Niu
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Niu, MQ., Chen, LQ. Nonlinear vibration isolation via a compliant mechanism and wire ropes. Nonlinear Dyn 107, 1687–1702 (2022). https://doi.org/10.1007/s11071-021-06588-9

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