Stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion

This paper presents the theory and application of the generalized polynomial chaos expansion for the stochastic free vibration of orthotropic plates. Specifically, the stochastic analysis of orthotropic plates under the uncertainties in elasticity moduli is investigated. The uncertain moduli, eigen-frequencies and eigen-modes of the plates are represented by truncated polynomial chaos expansions with arbitrary random basis. The expansions are substituted in the governing differential equations to calculating the polynomial chaos coefficients of the eigen-frequencies and the eigen-modes. Distribution functions of the uncertain moduli are derived from experimental data where the Pearson model is used to identify the type of density functions. This realization then is employed to construct random orthogonal basis for each uncertain parameter. Because of available experimental modal analysis data, this paper provides a useful practical example on the efficacy of polynomial chaos where the statistical moments and the probability distributions of modal responses are compared with experimental results.