基于复阻尼模型等效的黏性阻尼模型时域计算方法

doi:10.16183/j.cnki.jsjtu.2020.031

摘要/Abstract

摘要：

复阻尼模型的阻尼矩阵构造容易,仅依赖于材料损耗因子和结构刚度矩阵,但具有时域发散、非因果性等缺陷.从结构的固有特征恒定出发,推导了材料损耗因子与结构阻尼比的等效关系,进而得到与复阻尼模型等效的黏性阻尼模型.该阻尼模型不仅克服了复阻尼模型的缺陷,同时保留了复阻尼模型直接依赖材料损耗因子的便捷性.针对比例阻尼体系,依据材料损耗因子和结构振型阻尼比的关系,提出了基于复阻尼模型等效的黏性阻尼模型实振型叠加法.针对非比例阻尼体系,依据材料损耗因子和子结构振型阻尼比的关系,借助分块Rayleigh阻尼和状态空间法,提出了基于复阻尼模型等效的黏性阻尼模型复振型叠加法.通过算例分析验证了本文方法的可行性和正确性.

关键词: 复阻尼, 黏性阻尼, 等效, 损耗因子, 振型阻尼比

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

中图分类号:

TU311.3

孙攀旭, 杨红, 赵志明, 刘庆林. 基于复阻尼模型等效的黏性阻尼模型时域计算方法[J]. 上海交通大学学报, 2021, 55(6): 672-680.

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.

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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