Evaluation of PDF of Eigenvalue for Multibody System with Random Parameters

Dynamic characteristics of linear structural systems are governed by the natural frequencies and the mode-shapes. The study of probabilistic characterization of the eigensolutions of random matrix and differential operators is now an important research topic in the field of stochastic structural mechanics. In this paper, a new approach for the evaluation of the probability density function (pdf) of random eigenvalue for multibody system with random parameters is presented. At first, the random eigenvalue for multibody system with random parameters is computed by using transfer matrix method of multibody system. Then, the kernel density maximum entropy (MaxEnt) method is presented, which approximates the target pdf as a convex linear combination of kernel densities, transforming the original MP into a discrete MP, which is solved through a MaxEnt approach. In this way, simply solving a discrete MaxEnt problem, not requiring the evaluation of numerical integrals, an approximating pdf converging toward the MaxEnt pdf is obtained. The simulation results are validated by experiment results. All the numerical applications show the goodness and efficacy of the proposed procedure.