Modal Analysis of Random Structural Systems

This paper presents a method for computing the statistical variance of a structural system's eigenvalues and eigenvectors by component mode synthesis. The method relies on a modal summation to obtain engenvector derivatives where the contributions of individual modes are shown to diminish in importance as their natural frequencies become further separated from that of the eigenvector being differentiated. The convergence of mean eigenvalues and eigenvectors and their standard deviations is evaluated as the number of component modes used in the syntheses is increased. It is found that convergence proceeds in that order, with the standard deviations of eigenvectors requiring the largest number of modes for convergence. Numerical investigations show that the standard deviations of eigenvectors tend to converge for the first several modes when only a small fraction of the total number of component modes are taken into account. The dependence of convergence on the distribution of randomness and its spatial correlation is considered.