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

A simple explicit solution technique for problems in structural dynami cs, based on Heun's numerical method for ordinary differential equatio ns, is developed. The resulting conditionally stable modified Heun met hod (MHM) is easily implemented and provides a more accurate dynamic r esponse than the modified Euler's method. To examine the effectiveness , strengths, and limitations of MHM, error analyses for the natural pe riod, the displacement, the velocity and associated phase angle for a free and undamped simple mass-spring system are derived. Numerical exa mples for a single-degree-of-freedom system and a multi-degree-of-free dom (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 calculat ed.