Elimination of Overshoot in Forced Vibration Responses for Chang Explicit Family Methods

Abstract

An unusual overshooting behavior might be experienced in the forced response of a high-frequency mode for a structure-dependent integration method. This unusual overshooting is different from that found in the free vibration response and can be detected by examining an alternative form of the local truncation error derived from a forced vibration response rather than a free vibration response. In addition, this local truncation error can be applied to develop an effective remedy to remove the adverse overshoot behavior. This remedy can be obtained by introducing a load-dependent term into the difference equation for displacement increment for structure-dependent integration methods, such as the first and second Chang family methods. All the analytical findings are numerically verified.