A reduced-order random matrix approach for stochastic structural dynamics

The analysis of uncertainty of very large dynamical systems over a wide range of frequency is a significant challenge. In this paper a new reduced-order computational approach for very large damped stochastic linear dynamical systems is proposed. The approach is based on transformation and reduction of the stochastic system in the modal domain. A Wishart random matrix distribution is considered for the eigensolution of the reduced-order system. The identification of the parameters of the Wishart random model has been discussed. The newly proposed approach is compared with the existing random matrix models using numerical case studies. Results from the new approach have been validated using an experiment on a vibrating plate with randomly attached spring-mass oscillators. One hundred nominally identical samples have been physically created and individually tested within a laboratory framework. A simple step-by-step simulation method for implementing the new computational approach in conjunction with general purpose finite element software has been outlined. The method is applied to an aircraft wing problem with uncertainty to illustrate the generality, portability and the non-intrusive nature of the proposed approach.