Errors in Numerical Solution of Equation of Motion of Lightly Damped Sdof System Near Resonance

This study investigates the error which occurs when numerically integrating the equation of motion of a single degree of freedom system excited by a harmonic force near resonance. The Constant Average Acceleration method was considered in particular as it features in many finite element software packages. It was found that a considerable error in the calculated responses occurs in systems with low damping due to the well known phenomenon of period elongation. However, the error is reduced for systems with higher damping and/or when smaller time step is used. With regard to this, recommendations are given as to the time steps required to obtain solutions with a pre-defined level of accuracy.