Free vibration of a composite plate with spatially varying Gaussian properties under uncertain thermal field using assumed mode method

The stochastic assumed mode (SAM) method is developed for vibration analysis of composite plates with spatially varying stochastic properties. Temperature distribution in the plate is considered as Gaussian random field. To keep the generality, material properties of the composite plate such as tensile modulus, shear modulus, and thermal expansion coefficient are also assumed to be Gaussian random fields. Considering exponential autocovariance and employing the Karhunen–Loeve theorem, Gaussian random fields are decomposed. Hamilton principle and Euler–Lagrange equations are employed to derive stochastic equations of motion. The effects of uncertainties in mechanical properties as well as stochastic thermal preload on the natural frequencies are studied utilizing the Monte Carlo approach. Results show the proposed method can span probability space without a reduction in accuracy of the statistical moments in the case of plates with spatially stochastic properties. A significant decrease in computational cost in comparison with the intrusive stochastic finite element method (SFEM) is achieved.