Abstract
Quasi-zero-stiffness (QZS) vibration isolator seeks better isolation performance by lowering the natural frequency while maintaining the same static load bearing capacity as equivalent linear isolator. In previous works on QZS isolator, the steady-state response is usually assumed to be a single harmonic at the excitation frequency. However, the QZS isolator can actually exhibit various nonlinear dynamic behaviors such as multi-period responses and chaos. Even the simplest period-1 response, which occurs under most parameter conditions, is not a single harmonic, but contains superharmonics. This paper focuses on the superharmonic resonance that exists in the period-1 response. Both numerical simulation and analytical analysis are conducted; it is shown that there exist multiple superharmonics in the response, the frequencies of which are odd times the excitation frequency, but they are not very apparent when the excitation frequency is higher than a certain value. To characterize the overall properties of these superharmonics, two indices are proposed and analyzed in this paper. In addition, effect of superharmonic resonance on the vibration isolation performance is investigated based on the redefined transmissibility.
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References
Shaw, A.D., Neild, S.A., Wagg, D.J.: Dynamic analysis of high static low dynamic stiffness vibration isolation mounts. J. Sound Vib. 332, 1437–1455 (2013)
Ibrahim, R.A.: Recent advances in nonlinear passive vibration isolators. J. Sound Vib. 314, 371–452 (2008)
Liu, C.R., Yu, K.P.: A high-static-low-dynamic-stiffness vibration isolator with the auxiliary system. Nonlinear Dyn. 94, 1549–1567 (2018)
Liu, C.R., Yu, K.P., Pang, S.W.: A novel eight-legged vibration isolation platform with dual-pyramid-shape struts. Meccanica 54, 873–899 (2019)
Fu, N., Meng, L.S., Wu, W.J., Sun, J.G., Su, W.H., Meng, G., Rao, Z.S.: Recent advances in quasi-zero-stiffness vibration isolation systems. Appl. Mech. Mater. 397–400, 295–303 (2013)
Carrella, A., Brennan, M.J., Waters, T.P.: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 301, 678–689 (2007)
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, 707–717 (2009)
Carrella, A., Brennan, M.J., Waters, T.P.: Optimization of a quasi-zero-stiffness isolator. J. Mech. Sci. Technol. 21, 946–949 (2007)
Kovacic, I., Brennan, M.J., Waters, T.P.: A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. J. Sound Vib. 315, 700–711 (2008)
Hao, Z.F., Cao, Q.J.: The isolation characteristics of an archetypal dynamical model with stable-quasi-zero-stiffness. J. Sound Vib. 340, 61–79 (2015)
Lan, C.C., Yang, S.A., Wu, Y.S.: Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads. J. Sound Vib. 333, 4843–4858 (2014)
Huang, X.C., Liu, X.T., Sun, J.Y., Zhang, Z.Y., Hua, H.X.: Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: a theoretical and experimental study. J. Sound Vib. 333, 1132–1148 (2014)
Liu, X.T., Huang, X.C., Hua, H.X.: On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. J. Sound Vib. 332, 3359–3376 (2013)
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, 031009 (2014)
Hu, D., Chen, L.Q.: Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dyn. 95, 2367–2382 (2018)
Huang, X.C., Liu, X.T., Hua, H.X.: On the characteristics of an ultra-low frequency nonlinear isolator using sliding beam as negative stiffness. J. Mech. Sci. Technol. 28, 813–822 (2014)
Robertson, W.S., Kidner, M.R.F., Cazzolato, B.S., Zander, A.C.: Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation. J. Sound Vib. 326, 88–103 (2009)
Xu, D.L., Yu, Q.P., Zhou, J.X., Bishop, S.R.: Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 332, 3377–3389 (2013)
Wu, W.J., Chen, X.D., Shan, Y.H.: Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness. J. Sound Vib. 333, 2958–2970 (2014)
Li, Q., Zhu, Y., Xu, D.F., Hu, J.C., Min, W., Pang, L.C.: A negative stiffness vibration isolator using magnetic spring combined with rubber membrane. J. Mech. Sci. Technol. 27, 813–824 (2013)
Zheng, Y.S., Zhang, X.N., Luo, Y.J., Zhang, Y.H., Xie, S.L.: Analytical study of a quasi-zero stiffness coupling using a torsion magnetic spring with negative stiffness. Mech. Syst. Signal. Process. 100, 135–151 (2018)
Zhu, T., Cazzolato, B., Robertson, W.S.P., Zander, A.: Vibration isolation using six degree-of-freedom quasi-zero stiffness magnetic levitation. J. Sound Vib. 358, 48–73 (2015)
Kim, K.R., You, Y.H., Ahn, H.J.: Optimal design of a QZS isolator using flexures for a wide range of payload. Int. J. Precis. Eng. Manuf. 14, 911–917 (2013)
Ahn, H.J., Lim, S.H., Park, C.K.: An integrated design of quasi-zero stiffness mechanism. J. Mech. Sci. Technol. 30, 1071–1075 (2016)
Zhou, J.X., Xu, D.L., Bishop, S.: A torsion quasi-zero stiffness vibration isolator. J. Sound Vib. 338, 121–133 (2015)
Wang, X.L., Zhou, J.X., Xu, D.L., Ouyang, H.J., Duan, Y.: Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dyn. 87, 633–646 (2017)
Wang, Y., Li, S.M., 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, 635–654 (2017)
Carrella, A., Brennan, M.J., Waters, T.P., Lopes Jr., V.: Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. Int. J. Mech. Sci. 55, 22–29 (2012)
Levinson, N.: Transformation theory of non-linear differential equations of the second order. Ann. Math. 45, 723–737 (1944)
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The authors would like to thank Prof. Zhao for the helpful suggestions on the results presented in this paper.
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Liu, C., Yu, K. Superharmonic resonance of the quasi-zero-stiffness vibration isolator and its effect on the isolation performance. Nonlinear Dyn 100, 95–117 (2020). https://doi.org/10.1007/s11071-020-05509-6
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DOI: https://doi.org/10.1007/s11071-020-05509-6