Comparison of numerical integration methods in the linear dynamic analysis

Abstract

Direct integration methods for ordinary differential equations encountered in analysis of dynamic problems of vibration are studied and compared. Examples considered are a single degree of freedom oscillator and a multi degree of freedom linear model of vehicle with seven degree of freedom. The time-integrators used include both explicit and implicit methods of Runge-Kutta, Newmark, Wilson, the central difference method. The fourth-order Runge-Kutta method has been the preferred numerical integration scheme for solving linear single degree of freedom system or two degree of freedom systems. This method is very accurate, but requires very small time-steps and four equation solutions per time-step. These drawbacks hinder the solution of problems in multi degree of freedom systems, therefore implicit methods are considered for multi degree of freedom. Methods are compared in terms of accuracy and ease of formulation.