Damping Methodology for Condensed Solid Rocket Motor Structural Models

Abstract

ESA’s new small launcher – VEGA – has been designed as a single body launcher with three solid rocket motor stages and an additional liquid propulsion upper module used for attitude and orbit control, and satellite release. Part of the mission analysis is the so-called launcher-satellite coupled loads analysis which aims at computing the dynamic environment of the satellite for the most severe load cases in flight. To allow such analyses to be processed in short time, all stages of the launcher finite element model are condensed. The condensed launcher mathematical model can subsequently be coupled to a condensed satellite mathematical model. To obtain accurate predictions of the satellite dynamic environment it is evident that the damping of the entire system has to be defined in a representative way. This paper explains a methodology to compute the modal damping matrix of a superelement on the basis of the structural damping ratios assigned to the various materials in the associated finite element model and the associated complex strain energy of the modeshapes. The methodology turns out to be well suited for the computation of the modal damping matrix of condensed solid rocket motor structural models, as evidenced by correlation with firing tests conducted for the first stage motor of the VEGA launcher.