DYNAMIC ANALYSES OF MULTIPLE-DEGREE-OF-FREEDOM STRUCTURES USING A MODIFIED HEUN METHOD

A simple explicit solution technique for problems in structural dynamics, based on Heun's numerical method for ordinary differential equations, is developed. The resulting conditionally stable modified Heun method (MHM) is easily implemented and provides a more accurate dynamic response than the modified Euler's method. To examine the effectiveness, strengths, and limitations of MHM, error analyses for the natural period, the displacement, the velocity and associated phase angle for a free and undamped simple mass-spring system are derived. Numerical examples for a single-degree-of-freedom system and a multi-degree-of-freedom (MDOF) system are presented. In direct integration of MDOF systems, the amplitude decay characteristic exhibited by MHM provides a total system solution in which the low mode response is accurately calculated.