Wave propagation in uncertain laminated structure through stochastic wave finite element method

Abstract

In this paper, the composite beam is modeled in the case of the laminated material for the bending vibration. An analytical formulation is offered and used to extract the stiffness and mass matrices which will be injected in the dynamical equilibrium of the structure in order to apply the Wave Finite Element (WFE) method and characterize the dispersion curves corresponding to the bending vibration in the laminated beam. In order to rigorously describe the uncertainties in the mechanical and geometric parameters, the probabilistic tools are used. The study of the uncertain parameters is offered through the Monte Carlo techniques which can be used as a reference for statistical methods. Our methodology consists on producing a Gaussian distribution of random variables and simulating several draws of the dispersion curves using the WFE method according to the modeling of the composite beam. The Monte Carlo simulations lead to the calculation of the mean and the standard deviation of the wave number. The stochastic analytical development is formulated and exploited to validate the WFE results through the determination of the statistics of the dispersion curves using Monte Carlo simulations and explicit formulas.