Research on linear/nonlinear viscous damping and hysteretic damping in nonlinear vibration isolation systems

doi:10.1007/s10483-020-2630-6

Abstract

Abstract: A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance. In this paper, a generalized vibration isolation system is established with nonlinear stiffness, nonlinear viscous damping, and Bouc-Wen (BW) hysteretic damping. An approximate analytical analysis is performed based on a harmonic balance method (HBM) and an alternating frequency/time (AFT) domain technique. To evaluate the damping effect, a generalized equivalent damping ratio is defined with the stiffness-varying characteristics. A comprehensive comparison of different kinds of damping is made through numerical simulations. It is found that the damping ratio of the linear damping is related to the stiffness-varying characteristics while the damping ratios of two kinds of nonlinear damping are related to the responding amplitudes. The linear damping, hysteretic damping, and nonlinear viscous damping are suitable for the small-amplitude, medium-amplitude, and large-amplitude conditions, respectively. The hysteretic damping has an extra advantage of broadband isolation.

Key words: vibration isolation, nonlinear damping, Bouc-Wen (BW) model, harmonic balance method (HBM) Chinese Library

2010 MSC Number:

74H45

Zhong ZHANG, Muqing NIU, Kai YUAN, Yewei ZHANG. Research on linear/nonlinear viscous damping and hysteretic damping in nonlinear vibration isolation systems. Applied Mathematics and Mechanics (English Edition), 2020, 41(7): 983-998.

TrendMD

References

[1] LU, Z. Q., YANG, T. J., BRENNAN, M. J., LIU, Z. G., and CHEN, L. Q. Experimental investigation of a two-stage nonlinear vibration isolation system with high-static-low-dynamic stiffness. Journal of Applied Mechanics-Transactions of the ASME, 84, 021001(2017)
[2] XUE, J. R., ZHANG, Y. W., DING, H., and CHEN, L. Q. Vibration reduction evaluation of a linear system with a nonlinear energy sink under harmonic and random excitation. Applied Mathematics and Mechanics (English Edition), 41(1), 1-14(2020) https://doi.org/10.1007/s10483-020-2560-6
[3] QU, Y. G., XIE, F. T., and MENG, G. Nonlinear dynamic and acoustic analysis of orthogonally stiffened composite laminated cylindrical shells containing piecewise isolators. Journal of Sound and Vibration, 456, 199-220(2019)
[4] LU, Z. Q., BRENNAN, M., DING, H., and CHEN, L. Q. High-static-low-dynamic-stiffness vibration isolation enhanced by damping nonlinearity. Science China Technological Sciences, 62, 1103-1110(2019)
[5] MORADPOUR, S. and DEHESTANI, M. Optimal DDBD procedure for designing steel structures with nonlinear fluid viscous dampers. Structures, 22, 154-174(2019)
[6] CHEN, X. Q., SHEN, Z. P., HE, Q. S., DU, Q., and LIU, X. E. Influence of uncertainty and excitation amplitude on the vibration characteristics of rubber isolators. Journal of Sound and Vibration, 377, 216-225(2016)
[7] LU, Z. Q., HU, G. S., DING, H., and CHEN, L. Q. Jump-based estimation for nonlinear stiffness and damping parameters. Journal of Vibration and Control, 25, 325-335(2019)
[8] TANG, B. and BRENNAN, M. J. A comparison of two nonlinear damping mechanisms in a vibration isolator. Journal of Sound and Vibration, 332, 510-520(2013)
[9] HO, C., LANG, Z. Q., and BILLINGS, S. A. A frequency domain analysis of the effects of nonlinear damping on the Duffing equation. Mechanical Systems and Signal Processing, 45, 49-67(2014)
[10] YANG, J., XIONG, Y. P., and XING, J. T. Vibration power flow and force transmission behaviour of a nonlinear isolator mounted on a nonlinear base. International Journal of Mechanical Sciences, 115, 238-252(2016)
[11] LV, Q. B. and YAO, Z. Y. Analysis of the effects of nonlinear viscous damping on vibration isolator. Nonlinear Dynamics, 79, 2325-2332(2015)
[12] HUANG, X. C., SUN, J. Y., HUA, H. X., and ZHANG, Z. Y. The isolation performance of vibration systems with general velocity-displacement-dependent nonlinear damping under base excitation:numerical and experimental study. Nonlinear Dynamics, 85, 777-796(2016)
[13] BREWICK, P. T., MARSI, S. F., CARBONI, B., and LACARBONARA, W. Data-based nonlinear identification and constitutive modeling of hysteresis in nitinol and steel strands. Journal of Engineering Mechanics, 142, 04016107(2016)
[14] ZHAO, Z. W., WU, J. J., LIANG, B., LIU, H. Q., and SUN, Q. W. Numerical investigations on mechanical behavior of friction damped post-tensioned steel connections. Archive of Applied Mechanics, 88, 2247-2260(2018)
[15] FOTI, F., MARTINELLI, L., and PEROTTI, F. A new approach to the definition of self-damping for stranded cables. Meccanica, 51, 2827-2845(2016)
[16] AMJADIAN, M. and AGRAWAL, A. K. Modeling, design, and testing of a proof-of-concept prototype damper with friction and eddy current damping effects. Journal of Sound and Vibration, 413, 225-249(2018)
[17] GU, X. Y., YU, Y., LI, Y. C., LI, J. C., ASKARI, M., and SAMALI, B. Experimental study of semi-active magnetorheological elastomer base isolation system using optimal neuro fuzzy logic control. Mechanical Systems and Signal Processing, 119, 380-398(2019)
[18] KIANI, M. and VASEGHI-AMIRI, J. Effects of hysteretic damping on the seismic performance of tuned mass dampers. Structural Design of Tall and Special Buildings, 28, e1555(2019)
[19] ZHANG, Y. W., XU, K. F., ZANG, J., NI, Z. Y., ZHU, Y. P., and CHEN, L. Q. Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions. Applied Mathematics and Mechanics (English Edition), 40(12), 1791-1804(2019) https://doi.org/10.1007/s10483-019-2548-9
[20] MARKOU, A. A. and MANOLIS, G. D. Mechanical formulations for bilinear and trilinear hysteretic models used in base isolators. Bulletin of Earthquake Engineering, 14, 3591-3611(2016)
[21] SAUTER, D. and HAGEDORN, P. On the hysteresis of wire cables in Stockbridge dampers. International Journal of Non-Linear Mechanics, 37, 1453-1459(2002)
[22] CASINI, P. and VESTRONI, F. Nonlinear resonances of hysteretic oscillators. Acta Mechanica, 229, 939-952(2018)
[23] BARBIERI, N., BARBIERI, R., SILVA, R. A., MANNALA, M. J., and BARBIERI, L. S. V. Nonlinear dynamic analysis of wire-rope isolator and Stockbridge damper. Nonlinear Dynamics, 86, 501-512(2016)
[24] CARBONI, W. and LACARBONARA, W. Nonlinear vibration absorber with pinched hysteresis:theory and experiments. Journal of Engineering Mechanics, 142, 04016023(2016)
[25] SOLOVYOV, A. M., SEMENOV, M. E., MELESHENKO, P. A., and BARSUKOV, A. I. BoucWen model of hysteretic damping. Procedia Engineering, 201, 549-555(2017)
[26] LIU, T., BRISEGHELLA, B., ZHANG, Q. L., and ZORDAN, T. Equivalent damping of bilinear hysteretic SDOF system considering the influence of initial elastic damping. Soil Dynamics and Earthquake Engineering, 97, 74-85(2017)
[27] 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)
[28] CHEN, Y. Y., YAN, L. W., SZE, K., Y., and CHEN, S. H. Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems. Applied Mathematics and Mechanics (English Edition), 33(9), 1137-1152(2012) https://doi.org/10.1007/s10483-012-1611-6
[29] ZHANG, Y. W., LU, Y. N., ZHANG, W., TENG, Y. Y., YANG, H. X., YANG, T. Z., and CHEN, L. Q. Nonlinear energy sink with inerter. Mechanical Systems and Signal Processing, 125, 52-64(2019)
[30] JIANG, W. N., ZHANG, G. C., and CHEN, L. Q. Forced response of quadratic nonlinear oscillator:comparison of various approaches. Applied Mathematics and Mechanics (English Edition), 36(11), 1403-1416(2015) https://doi.org/10.1007/s10483-015-1991-7
[31] XIONG, H., KONG, X. R., LI, H. Q., and YANG, Z. G. Vibration analysis of nonlinear systems with the bilinear hysteretic oscillator by using incremental harmonic balance method. Communications in Nonlinear Science and Numerical Simulation, 42, 437-450(2017)
[32] WU, R. P., BAI, H. B., and LU, C. H. Simplified analysis of hysteresis dry friction vibration isolation system on flexible foundation (in Chinese). Journal of Mechanical Strength, 41, 44-48(2019)
[33] WONG, C. W., NI, Y. Q., and LAU, S. L. Steady-state oscillation of hysteretic differential model, I:response analysis. Journal of Engineering Mechanics, 120, 2271-2298(1994)
[34] YUAN, T. C., YANG, J., and CHEN, L. Q. A harmonic balance approach with alternating frequency/time domain progress for piezoelectric mechanical systems. Mechanical Systems and Signal Processing, 120, 274-289(2019)
[35] ZHANG, Z. Y. and CHEN, Y. S. Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamic system with fractional exponential. Applied Mathematics and Mechanics (English Edition), 35(4), 423-436(2014) https://doi.org/10.1007/s10483-014-1802-9
[36] IKHOUANE, F., EURTADO, J. E., and RODELLAR, J. Variation of the hysteresis loop with the Bouc-Wen model parameters. Nonlinear Dynamics, 48, 361-380(2007)