Probabilistic analysis of non-self-adjoint mechanical systems with uncertain parameters

new approach to analyze mechanical systems that have an uncertain distribution of material prope:rties and loadings, for the variability of their dynamic response parameters is developed. The methodology is demonstrated through solving for the probabilistic moments of eigenvalues of a non-self-adjoint structural system. Material properties are modelled using random fields and uncertain loadings are modelled using random variables. By treating the random fluctuations of vibratory response to be the stochastic perturbations to mean response, second order moments of eigenvalues are obtained. To circumvent the practical difficulty of obtaining the exact correlation models for parameter variability, second order moments of eigenvalues are evaluated in terms of variance functions. Both the sensitivity of eigenvalues to the variability in system parameters, and the effects on the eigenvalue variability of correlation properties of uncertain parameters are demonstrated.