Composite Implicit Time Integration Method for Nonviscous Damping Structural Dynamic System

Abstract

A nonviscous damping model uses convolution to account for the complete velocity history. The displacement response, velocity response, and acceleration response of a system with nonviscous damping are usually computed by modified direct integration methods. However, existing direct integration methods often come with strong numerical damping that reduces the accuracy of calculated responses. An improved composite direct integration method based on the Bathe method is proposed in this study. In this method, the convolution of the nonviscous damping is computed using Simpson’s rule to improve the accuracy. The combination of Simpson’s rule and the Bathe method almost doubles the efficiency of the calculation of responses. Nonviscous damping of two moments can be computed within one loop calculation of the convolution. Compared with existing direct integration methods, the accuracy can be improved using the proposed method. Moreover, a simplified method is proposed to improve the efficiency of response calculation for the exponential kernel nonviscous damping system. The simplified method can improve the efficiency of computation greatly. Examples are used to validate the performance of the extended composite direct integration and simplified method.