Dynamic Analysis of Structures With Random Properties by Component Mode Synthesis

This paper presents a method for computing the statistical variance of eigenvalues and eigenvectors by component mode synthesis. The method relies on a modal summation to obtain eigenvector 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 synthesis 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. However, numerical investigations have shown that even the standard deviations of eigenvectors tend to converge for the first several system modes, when only a small fraction of the total number of component modes is taken into account. The dependence of convergence on the distribution of randomness and its spatial correlation is also discussed.