Abstract Summary
This paper is concerned with the prediction of the high frequency shock response of a complex system that has uncertain properties. A fundamental aspect of the method is the representation of the response in a combination of the time and frequency domains. This type of description is commonly used in predicting the response of a deterministic system to non-stationary random excitation (for example in earthquake dynamics), where a formalism known as the Priestley spectrum is used. However the present concern is with the deterministic transient loading of a random system and it is not entirely obvious that a description in the form of the Priestley spectrum can be employed – the random ensemble involved is the ensemble of random systems rather than the ensemble of random loading. It is shown here that an approach which is completely analogous to the Priestley spectrum can in fact be applied to the present problem, and this forms the basis for the derivation of a set of transient statistical energy analysis (TSEA) which govern the system response. The equations predict both the mean and variance of the system response, the system randomness being described by a model based on the Gaussian Orthogonal Ensemble (GOE) of random matrices. The governing equations are presented and then applied to a range of example systems.
