Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

Abstract

In this study, the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method. The material properties including tensile modulus, shear modulus, and density of the plate were assumed to be spatially varying and uncertain. Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties. The stochastic fields were decomposed via application of the Karhunen-Loeve theorem. A first-order shear deformation theory was assumed, following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies. The stochastic equations of motion of the plate were obtained using the variational principle. The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies, and the corresponding mode shapes of the plate were determined using a polynomial chaos approach. The proposed method significantly reduced the size of the mathematical models of the structure, which is very useful for enhancing the computational efficiency of stochastic simulations. The methodology was verified using a stochastic finite element method and the available results in literature. The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated, and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.

Keywords

composite plate / spatially varying stochastic properties / Galerkin method / polynomial chaos approach / semi-analytical approach

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