Analysis of Eigenvalues and Modal Interaction of Stochastic Systems

An eigenvalue spectral analysis of stochastic engineering systems is presented. A comparative numerical study between approximations based on Monte Carlo sampling, a Taylor series-based perturbation approach, and the polynomial chaos representation is conducted. It is observed that the polynomial chaos representation gives more accurate estimates of the statistical moments than the perturbation method, especially for the higher modes. The differences of accuracy in the two methods are more pronounced as the system variability increases. Moreover, the chaos expansion gives a more detailed probabilistic description of the eigenvalues and the eigenvectors. In addition, a method for representing the statistical modal overlapping is presented that characterizes the statistical interaction between the various modes.