Uncertainty propagation analysis in free vibration of uncertain composite plate using stochastic finite element method

Abstract

Material uncertainty is more widespread in composite material than the other engineering materials. This uncertainty makes response of these types of structures to be nondeterministic. In order to predict structural reliability, uncertainty in structural responses must be quantified. There is not a reported research in the literature studing free vibration of composite plate with spatially stochastic material properties. In this research, physical and mechanical properties of composite plate including tensile and shear modulus and density of the plate are modeled as stochastic Gaussian fields. Assuming exponential auto covariance kernels for aforementioned stochastic fields, they are discretized to two parts, including deterministic and stochastic parts employing Karhunen-Loeve theorem. Assuming linear form of strains, mechanical strains are defined applying first order shear deformation theory. Kinetic and potential energy of the composite plate is extracted using finite element formulation. Stochastic finite element formulation is derived employing Hamilton’s principle and Euler-Lagrange and equations are verified with the results in the literature for deterministic case. After verification of formulation, material uncertainty effects on uncertainty of natural frequencies are investigated using Monte Carlo simulation. Results show that there is a linear relation between coefficient of variation of uncertain properties and coefficient of variation of stochastic natural frequencies.