Modeling and Forced Vibration of Smart Piezoelectric Beams Using Simple Higher Order Shear Deformation Theory

Document Type : Original Article

Authors

1 Egyptian Armed Forces, Egypt.

2 Libyan Armed Forces, Libya.

Abstract

In the current work, a finite element formulation is developed for modeling and forced vibration of isotropic as well as orthotropic composite beams with distributed piezoelectric actuators subjected to both mechanical and electrical loads. The proposed model is developed based on a simple higher order shear deformation theory where the displacements field equations in the model accounts for a parabolic distribution of the shear strain and the non-linearity of in-plane displacements across the thickness and subsequences the shear correction factor is not involved. The virtual displacement method is used to formulate the equations of motion of the structure system. The model is valid for both segmented and continuous piezoelectric elements which can be either surface bonded or embedded in the laminated beams. A two-node element with four mechanical degrees of freedom in addition to one electrical degree of freedom for each node is used in the finite element formulation. The electric potential is considered as function of the thickness and the length of the beam element. The steady state responses for damped and undamprd beams are formulated. A MATLAB code is developed to compute the static deformation, free vibration parameters, and the beams responses due to harmonic excitation of mechanical and electrical loads. The predictions from the proposed model are in good shape.

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