Generalized Wishart distribution for probabilistic structural dynamics

摘要

An accurate and efficient uncertainty quantification of the dynamic response of complex structural systems is crucial for their design and analysis. Among the many approaches proposed, the random matrix approach has received significant attention over the past decade. In this paper two new random matrix models, namely (1) generalized scalar Wishart distribution and (2) generalized diagonal Wishart distribution have been proposed. The central aims behind the proposition of the new models are to (1) improve the accuracy of the statistical predictions, (2) simplify the analytical formulations and (3) improve computational efficiency. Identification of the parameters of the newly proposed random matrix models has been discussed. Closed-form expressions have been derived using rigorous analytical approaches. It is considered that the dynamical system is proportionally damped and the mass and stiffness properties of the system are random. The newly proposed approaches are compared with the existing Wishart random matrix model using numerical case studies. Results from the random matrix approaches have been validated using an experiment on a vibrating plate with randomly attached spring-mass oscillators. One hundred nominally identical samples have been created and separately tested within a laboratory framework. Relative merits and demerits of different random matrix formulations are discussed and based on the numerical and experimental studies the recommendation for the best model has been given. A simple step-by-step method for implementing the new computational approach in conjunction with general purpose finite element software has been outlined. Keywords Unified uncertainty quantification - Random matrix theory - Wishart distribution - Model validation - Parameter identification