基于复阻尼理论的混合结构Rayleigh阻尼模型
Rayleigh Damping Model of Mixed Structures Based onComplex Damping Theory

混合结构的阻尼矩阵不满足经典阻尼条件，导致传统的模态叠加法法适用。复阻尼理论法适用于时域计算，其自由振动响应中存在发散现象。针对混合结构的阻尼矩阵非比例性和复阻尼理论的时域发散性，基于频域等效原则构建了求解Rayleigh阻尼系数的数学优化模型，进而得到与复阻尼理论等效的Rayleigh阻尼运动方程。算例分析表明：依据位移时程响应和结构等效阻尼比可证明Rayleigh阻尼运动方程的正确性。基于本文研究成果，等效复阻尼理论的混合结构Rayleigh阻尼运动方程可直接采用模态叠加法，结合其确定的结构等效阻尼比，为混合结构的振型分解反应谱法提供理论依据。
The traditional modal superposition method cannot be used to model mixed structures because the damping matrix of mixed structures does not meet the classical damping condition. In addition, the complex damping theory cannot be applied in time domain calculations because of the divergence in structural free vibration response. To solve these problems, in this paper, a mathematical optimization model for solving Rayleigh damping coefficients is constructed based on the frequency domain equivalence principle. Modal mass participation factors are used as weighting function and the coefficients are used as variables, which can be calculated by the mathematical model. The Rayleigh damping motion equation, which is equivalent to complex damping theory, is obtained. The calculated results show that the correctness of Rayleigh damping motion equation is proved according to the displacement-time history response and structural equivalent damping ratio. Based on the results of this study, the Rayleigh damping motion equation of mixed structures, which is equivalent to complex damping theory, can directly use the modal superposition method. Combined with structural equivalent damping ratios, it can provide a theoretical basis for mode-superposition response spectrum methods of mixed structures.