A time-domain method for free vibration responses of an equivalent viscous damped system based on a complex damping model

The free vibration responses are divergent based on a complex time-domain damping model. The traditional step by step integration method cannot be used to calculate the time-domain responses. Based on the theoretic solution that eliminates the divergent term for the complex damping model, the equivalent viscous damping model is proposed and the corresponding average acceleration method is realized in this paper. The numerical cases show that the calculated results of the equivalent viscous damped system are convergent, which are equal to the ones of the deleted divergent term based on the complex damping model. The correctness of the proposed method is verified, and the computational efficiency is high.

Automated summary

In this paper, the divergent behavior of free vibration responses is studied based on a complex time-domain damping model. The traditional step by step integration method is not applicable for calculating the time-domain responses. To overcome this limitation, an equivalent viscous damping model and the corresponding average acceleration method are proposed. Numerical cases demonstrate the convergence and correctness of the proposed method, as well as its high computational efficiency.