Shock Spectra of a Nonlinear System

Abstract

The peak response under pulse excitation, of a single-degree-of-freedom system with nonlinear spring approximated by two straight lines, is analytically determined. Shock spectra for the step and delta function are developed with damping as parameter. For the rectangular pulse excitation, the shock spectra for zero damping are presented with pulse duration as a parameter. For the arbitrary pulse shape, a general procedure is discussed and illustrated for the sine pulse of differing pulse duration. Generalized phase-plane plots associated with the problem are included. The shock spectra presented are applicable only when the first peak corresponds to the maximum response, thereby avoiding the questions of unloading.