Stochastic Modeling of Composite Structures Coupled with Piezoelectric Shunted Resistive Circuits

Lorrane Pereira Ribeiro¹; Antônio Marcos Gonçalves de Lima¹

¹ Universidade Federal de Uberlândia

doi:10.20906/CPS/COB-2015-0650

Resumo

This work is devoted to the stochastic finite element modeling of a composite structure containing piezoelectric element coupled with a shunt resistive circuit with the aim of passive vibration attenuation. The deterministic electromechanical problem is modeled by combining the First-Order Shear Deformation Theory, in order to approximate the mechanical displacement fields, with the so-called Layerwise Theory used to model the discrete electric fields within the composite element. 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