STUDY OF TIME STEPPING METHODS FOR STIFF SYSTEMS OF DYNAMIC EQUATIONS

Abstract

An undamped stiff two degree of freedom system is considered for this study. The solution methods of equilibrium equation includes mode superposition and some popular time stepping methods. The time history for various time stepping methods are obtained by the aid of computer programming in C++. Due to inherent property of stiff system higher frequency is obtained of the order of 100 times greater than the fundamental frequency. This leads to the time history obtained in high frequency as well as low frequency region. An aim is to get the accurate response in low frequency mode. Another aim is to filter out response in high frequency mode in as few time steps as possible. The popular time stepping methods are studied with respect to stability of solution, accuracy in first mode response and damping characteristics for higher mode response. The solutions obtained by the popular time stepping methods for the two degree of freedom undamped system. are compared with the exact response obtained by mode superposition for the undamped case. The strengths and weaknesses of the time stepping methods studied in chapter 4.