PEDEM: a new method for the analysis of the stochastic response

Abstract

The analysis of the response of a stochastic system, through a discrete coordinate representation, can become computationally challenging, even by using a full modal representation; in fact, many dynamic load cases have stochastic behaviour as the wall pressure fluctuations due to the turbulent boundary layer. In the present work, a new method is presented and discussed and it is named frequency modulated pseudo equivalent deterministic excitation (PEDEM). PEDEM is based on the pseudo excitation method (PEM), but it tries to overcome the computational neck-bottles of this latter by introducing some approximations which are based on the analysis of the eigensolutions of the dynamic load matrix versus frequency. The solution approach uses three different approximations for the load matrix with reference to three frequency ranges, named low, mid and high; these approximations derive from the eigenanalysis of the load matrix. A criterion to identify the three frequency ranges is proposed, too and it is expressed in terms of a reduced dimensionless frequency. PEDEM is thus applied to a plate response; this test case that contains the most relevant parameters of a structural problem. The results herein discussed show that the correlation area can play a fundamental role in discriminating the quality of the approximation. A good level of accuracy and representation of the stochastic system together with a significant reduction of the computational costs are obtained if compared to a full stochastic response (FSR) or PEM solution.