Time Integration Schemes in Dynamic Problems: Effect of Damping on Numerical Stability and Accuracy

摘要

A great deal of progress has been made in the past several decades towards the understanding and development of time integration methods in structural dynamics. These methods involves a step by step algorithm for transient analysis of linear and non-linear dynamic problems. It is essential to provide a comprehensive survey of various methodologies used to solve second order differential equations in a single article. Broadly, the methods include direct integration, mode superposition and response spectrum methods among others. The first two methods uses an integration scheme while response spectrum method is based on extreme response analysis. Both direct integration and mode superposition method use an integration scheme but the selection of a particular method depends on the problem and frequency content of the loading. A detailed survey of various integration schemes is presented in this paper. The stability and accuracy of these integration schemes has been studied by researches in the past. However, the effect of damping on the stability and accuracy of these schemes need to be investigated. A single degree of freedom system is used to check the stability and accuracy criteria of various integration schemes. Also, the effect of damping on these parameters is studied and results are presented.