Dynamic and Vibration Analysis of Composite Timoshenko Beam with Piezoelectric Layers

Beams are the basic geometries in engineering and many engineering issues are simplified as a beam problem. In this paper, the dynamics and vibration analysis of composite Timoshenko beam made of epoxy graphite layers with two piezoelectric layers on both sides have been investigated. Extraction of motion equations has been conducted based on the first-order shear deformation beam theory using the Hamilton principle. The partial differential equations were converted to the first-order coupled differential equations and then they were solved by fourth-order Runge–Kutta method. The effect of piezoelectric parameters on the vibrational and dynamic response of the beam has been investigated. The results show that the natural frequency of the beam decreases with increasing the length of the neam. Among piezoelectric parameters, the parameter of C11 has a lower effect than the effective transverse coefficient of e31 in the frequency response. As the ratio of the length of the beam is lower than the thickness, the effect of C11 will be greater on the natural frequency. The effect of the other piezoelectric parameters in the frequency response has also been evaluated very small relative to these two parameters.