Application of the Transient Finite Energy Method to Spacecraft Structures for Shock Environment Predictions

Abstract

The modern spacecraft will encounter multiple mechanical shock events over the course of its mission, from the modest but repetitive jolts of ground transportation to the extreme accelerations produced by pyrotechnic devices during stage separation and deployment. These transient shock events have the potential to damage sensitive hardware and degrade functional performance, making it necessary to accurately characterize and predict the shock environment at critical locations throughout the structure. This research investigates the application of the Transient Finite Energy (TFE) method to predict shock response at remote structural locations resulting from a known Shock Response Spectrum (SRS) source specification. The TFE method operates across the SRS, time, and frequency domains, using a Finite Element Model (FEM) coupled with frequency-domain force recovery to transform an SRS source specification into physically meaningful forcing functions that preserve the temporal and spectral content discarded by conventional SRS-based methods. The TFE method takes advantage of the fact that an infinite number of time histories can satisfy a specified SRS. By applying many forcing functions with unique properties, a mean SRS response may be computed. The central physical premise is that each shock event imparts a finite impulse, a finite quantity of momentum transferred in a brief time window, even though the amplitude, rise time, and duration of individual events are statistical in nature. This finite-energy constraint lends the method its name and provides a bound on the recovered forces. Analytical capability for predicting shock environments using the TFE method has shown promise; however, the workflow introduces a chain of modeling decisions whose individual and combined influence on prediction quality must be understood before results can be trusted. This work seeks to make those assumptions explicit by examining the fundamentals of the TFE workflow and applying the method to a validated cantilever beam model to predict the shock environment at a remote response location and evaluate how the structural dynamics reshape the transmitted shock.