Vibration of a simply supported functionally graded piezoelectric rectangular plate

The free and forced vibration of a functionally graded piezoelectric rectangular plate with exponent-law dependent material properties is studied in this paper. The displacements and electric potential of the plate are expanded in the forms of Fourier series and state equations are then established. Given simply supported and grounded edge boundary conditions, the exact frequency equations of free vibration of a functionally graded piezoelectric rectangular plate are derived and solved for several numerical examples. An exact solution of the coupling electroelastic fields in the plate under forced vibration is also obtained. The influences of the forced frequencies are then studied through examples.