A model for flrexural vibration of laminated beams embedded with piezoelectric layers including shear deformation

A beam embedded piezoelectric layers is widely used as actuator to excite or control the vibrations of machines and structures. It is also applied as sensor to measure vibrations. By using the hypothesis of Timoshenko beam theory and assuming the distribution of the electric potential in the z-direction, this paper derives the governing equations for sandwich beams coupled with piezoelectric layers. The eigen solution and frequency equation of the free vibration are then obtained for the beam with two simply supported ends and numerical results are also presented to demonstrate the availability of the presented method.