Steady-State Forced Vibration of Functionally Graded Piezoelectric Beams

The steady-state forced vibration of a functionally graded piezoelectric material beam under different loading (electrical, mechanical, and electromechanical) cases and different boundary conditions is studied. Sixteen kinds of situations are considered in the present article. The steady-state responses of the beams under forced mechanical or electric load are obtained by using the state-space-based differential quadrature method. In contrast to other investigations, the present work gets the results by a discrete method using the differential quadrature technique, which can easily get stable results. The results agree very well with other investigations found in some special cases. Finally, some properties of the beams under the corresponding load conditions are discussed.