Time-Domain Calculation Method of an Equivalent Viscous Damping Model Based on Complex Damping Model

doi:10.16183/j.cnki.jsjtu.2020.031

Abstract

Abstract:

The damping matrix of the complex damping model is easy to be constructed, which only depends on the material loss factor and the structural stiffness matrix. However, the complex damping model has some shortcomings, such as time-domain divergence and causality. Structural inherent characteristics are constant, so that the equivalent relationship between material loss factor and structural damping ratio is deduced and the viscous damping model which is equivalent to complex damping model is obtained. The proposed damping model overcomes the shortcoming of the complex damping model. Besides, the convenience that the complex damping model is directly dependent on material loss factor is retained. According to the equivalent relationship between the material loss factor and structural modal damping ratio, the real mode superposition method based on the proposed damping model is suggested for the proportional damping system. For the non-proportional damping system, according to the equivalent relationship between the material loss factor and modal damping ratio of the substructure, the complex mode superposition method based on the proposed damping model is proposed by the aid of Rayleigh damping and the state space method. The example analysis proves the feasibility and correctness of the proposed method.

Key words: complex damping, viscous damping, equivalent, loss factor, modal damping ratio

CLC Number:

TU311.3

SUN Panxu, YANG Hong, ZHAO Zhiming, LIU Qinglin. Time-Domain Calculation Method of an Equivalent Viscous Damping Model Based on Complex Damping Model[J]. Journal of Shanghai Jiao Tong University, 2021, 55(6): 672-680.

Figures/Tables 10

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层数	质量×10^-3/kg	刚度×10^-5/(N·m^-1)
1	5.0	3.0
2	4.0	2.5
3	3.0	2.0
4	2.0	1.5

参数	El Centro 波		Taft 波
参数	FFZ^[24]	EVR	FFZ^[24]	EVR
位移峰值时间/s	3.48	3.48	4.24	4.22
位移峰值/cm	10.0567	10.9170	5.6769	5.4814
峰值相对误差/%	—	8.55	—	3.44
加速度峰值时间/s	12.00	11.96	4.22	4.22
加速度峰值/(cm·s^-2)	252.0428	228.1943	209.7324	197.1087
峰值相对误差/%	—	9.46	—	6.02

层数	质量×10^-3/kg	刚度×10^-5/(N·m^-1)
1	3.0	2.0
2	2.0	1.5

参数	El Centro 波		Taft 波
参数	FFZ^[24]	EVC	FFZ^[24]	EVC
位移峰值时间/s	12.32	12.30	4.04	4.02
位移峰值/cm	5.3742	5.5797	3.0664	3.1938
峰值相对误差/%	—	3.82	—	4.15
加速度峰值时间/s	11.76	11.76	9.84	9.84
加速度峰值/(cm·簚s^-2)	351.1148	321.1245	217.1560	196.1360
峰值相对误差/%	—	8.54	—	9.68