Stochastic Modeling of Composite Structures Coupled with Piezoelectric Shunted Circuits

Lorrane Ribeiro¹; Antônio Marcos De Lima¹

¹ Universidade Federal de Uberlândia

doi:10.20906/CPS/USM-2016-0026

Resumo

In this work focus is given to the stochastic finite element modeling of a composite structure containing piezoelectric element coupled with a shunt circuit with the aim of passive vibration attenuation. So that, the parameters which introduce uncertainties in the model as the directions of the fibers, the thicknesses of the layers, the shunt circuit elements, resistance and inductance values, are taken as uncertain variables. First-Order Shear Deformation Theory combined with the so-called Layerwise Theory are used to model the deterministic electromechanical problem, in order to approximate the mechanical displacement fields and the discrete electric fields respectively. It must be emphasized that the deterministic finite element modeling procedure was performed taking into the parameterization process of the design variables of interest to be further assumed as random variables in a straightforward way. Thus, by using Stochastic Finite Element Method, uncertain variables were modeled as Gaussian stochastic homogeneous fields and discretized in accordance with the Karhunen-Loève series expansion method. By intervening directly in the process of integration, was possible to find the exact mass and stiffness matrices of the composite structure. The modeling procedure is confined to the frequency domain, and the dynamic responses are characterized by frequency response functions. To solve the stochastic problem, Monte Carlo simulation was used as stochastic solver combined with the sampling method called Latin Hypercube.

Palavras-chave: Stochastic modeling; Composite materials; Passive vibration control; Piezoelectric shunted circuits; Uncertainty propagation