Abstract: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.
