An Energy Conservation Algorithm for Nonlinear Dynamic Equation

Abstract

An energy conservation algorithm for numerically solving nonlinear multidegree-of-freedom (MDOF) dynamic equations is proposed. Firstly, by Taylor expansion and Duhamel integration, an integral iteration formula for numerically solving the nonlinear problems can be achieved. However, this formula still includes a parameter that is to be determined. Secondly, through some mathematical manipulations, the original dynamical equation can be further converted into an energy conservation equation which can then be used to determine the unknown parameter. Finally, an accurate numerical result for the nonlinear problem is achieved by substituting this parameter into the integral iteration formula. Several examples are used to compare the current method with the well-known Runge-Kutta method. They all show that the energy conservation algorithm introduced in this study can eliminate algorithm damping inherent in the Runge-Kutta algorithm and also has better stability for large integral steps.