• Biomechanics, Engineering and Interdiscipliary Mechanics •

### COMPLEX MODE SUPERPOSITION METHOD BASED ON FREQUENCY DEPENDENT VISCOUS DAMPING MODEL1)

Sun Panxu*, Yang Hong*2)(), Wu Jiafeng*, Wang Zhijun*

1. *(School of Civil Engineering, Chongqing University, Chongqing 400045, China)
(Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education, Chongqing University, Chongqing 400045, China)
• Received:2018-04-04 Accepted:2018-04-04 Online:2018-09-18 Published:2018-10-18
• Contact: Yang Hong

Abstract:

According to the viscous damping model, energy dissipation is related to external excitation frequencies in each cycle. There is divergence in time domain calculation results of complex damping model. In order to overcome the two kinds of disadvantages of damping models, frequency dependent damping model is obtained by time-frequency transformation principle on the basis of complex damping model. Energy dissipation is not related to external excitation frequencies in each cycle. In addition, time-history calculation of frequency dependent damping model is convergent. Real mode superposition method is not directly adopted, because the damping matrix of mixed structure of multiple damping characteristic materials is non-proportional. By the transformations of frequency dependent damping model and complex damping model, complex mode superposition method is proposed based on frequency dependent damping model. And it can be directly applied to mixed structure. The analysis results of the cases show that compared with complex mode superposition method based on viscous damping model, the calculation results of the complex mode superposition method based on frequency dependent damping model are unique. In addition, the method does not increase matrix dimensions and has high computational efficiency. The analysis results of small damping cases show that calculation results of the two methods are approximately equal. They are consistent with frequency domain calculation results of complex damping model. When the damping ratios are larger, the difference of calculation results by the two methods will increase. While the calculation results of complex mode superposition method based on frequency dependent damping model will remain consistent with frequency domain calculation results of complex damping model.

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