Joint Statistics of Natural Frequencies Corresponding to Structural Systems with Singular Random Parameter Matrices

Abstract

An asymptotic approximation methodology for solving standard random eigenvalue problems is generalized herein to account for structural systems with singular random parameter matrices. In this regard, resorting to the concept of the Moore–Penrose matrix inverse and generalizing expressions for the rate of change of the eigenvalues, novel closed-form expressions are derived for the joint moments of the system natural frequencies. Two indicative examples pertaining to multiple-degree-of-freedom structural systems are considered for demonstrating the reliability of the methodology. Comparisons with pertinent Monte Carlo simulation data are included as well.