Finite Element Modeling of Smart Timoshenko Beams with Piezoelectric Materials

Document Type : Original Article

Authors

Egyptian Armed Forces, Egypt.

Abstract

In the present work, a finite element model has been proposed to describe the response of isotropic and anisotropic smart beams with piezoelectric materials subjected to different mechanical loads as well as electrical load. The assumed field displacements of the beam are represented by First-order Shear Deformation Theory (FSDT), the Timoshenko beam theory. The equation of motion of the smart beam system is derived using the principle of virtual displacements. A hermit cubic shape function is used to represent the axial displacement u, the transverse displacement is represented by a quadratic shape function, and the normal rotation is represented by a linear shape function and the electric potential at each node. The shear correction factor is used to improve the obtained results. A MATLAB code is developed to compute the natural frequency and the static deformations of the structure system due to the applied mechanical and electrical loads at different boundary conditions. The obtained results obtained of the developed are compared to the available results of other investigators, good agreement is generally obtained.

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