Random Eigenvalue Problems in Structural Analysis

Abstract

A computerized Monte Carlo simulation is presented for calculating the statistical properties of the eigenvalues of a spring supported beam-column. The spring supports and axial force are treated as random variables ; the distributions of material and geometric properties are considered to be correlated homogeneous random functions. Each sample distribution is generated using a new method for simulating multivariate homogeneous random processes having a specified cross-spectral density matrix. This method of solution is used to investigate the accuracy of the perturbation method for calculating the variance of the nth vibration and buckling eigenvalues. Numerical results are presented for the case where the axial load is equal to 27 % of the fundamental buckling load and the distributions of material and geometric properties are uncorrelated. The perturbation method is shown to be acceptable for limited ranges of the statistical variations of properties.