Modeling and Analysis of Smart Timoshenko Beams with Piezoelectric materials

In the present work, a finite element model is proposed to describe the response of isotropic and orthotropic beams with piezoelectric actuators due to applied mechanical loads as well as electrical load. The assumed field displacements of the beams 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. In finite element formulation a cubic shape function is used to represent the axial displacement, the transverse displacement is represented by a quadratic shape function, while and the normal rotation and the electric potential is represented by a linear shape function at each node. The shear correction factor is used to improve the obtained results. A MATLAB code is developed to formulate the model and compute the natural frequency and the static deformation of the proposed structure system. The obtained results are compared to the available results of other investigators, good agreement is generally obtained.