Shock Response Spectrum and Its Damage Potential: An Application to Launch Vehicle Structures

Abstract

The present work briefly summarizes the analysis of pyrotechnic shocks encountered in launch vehicle structures using the shock response spectrum (SRS) and the pseudo velocity shock response spectrum techniques. The mathematical idealization assumes a single degree of freedom (SDOF) system model with base excitation. The mounting elements of SDOF system are assumed to be flexible and each mounting element can be described by its stiffness and damping parameters. The convolution integral approach is used for obtaining an analytical solution of the differential equation and later it is transformed to a digitized form using the techniques based on z-transform approach. The two different z-transform techniques which are used namely are Kelly-Richman algorithm which is based on the impulse invariant response and Smallwood algorithm which is based on the ramp invariant response, for assessing the numerical accuracy of the two different approaches in evaluating the shock response spectrum which indicates the peak response of each system with respect to the natural frequency of each system. Accuracy of the two numerical techniques discussed in this study are briefly applied to predict the shock response of the structure subjected to half-sine input base excitation and to an arbitrary base excitation recorded during a pyro-stage separation event.

Keywords: shock response spectrum, relative velocity spectrum, convolution integral,  z-transform, discrete solution