Parametric Probabilistic Approach in the Dynamics of Porous FGM Curved Beams

Abstract

In this article we evaluate the uncertain dynamic response of inhomogeneous curved beams constructed with ceramic and metallic materials that vary in a given functional forms. The construction process of this type of structures conducts to the presence of porosity in its domain. The porosity can be source of uncertainties in the dynamic behavior. In order to study the dynamics of these structures, we employed the Principle of Virtual Work to derive a curved beam model. The model incorporates shear flexibility, variable curvature and variable porosity. It serves as a mean deterministic reference to the studies on stochastic dynamics and uncertainty quantification, which are objectives of this article. The uncertainty quantification procedure considers the introduction of random variables to characterize the uncertainty in material or geometric properties such as elasticity modulus and/or density of the material constituents, curvature radius of the beam, porosity parameters, among others. The probability density functions (PDF) of the random variables are derived appealing to the Maximum Entropy Principle. Then, the probabilistic model is constructed with the basis of the deterministic model and both calculated within finite element approaches. Once the probabilistic model is constructed, the Monte Carlo Method is employed to calculate random realizations. In order to identify the sensitivity of the random parameters, a number of scenarios are evaluated in which the random variables can have different distributions/variations according to the level of information known or at least assumed.