Analytical Solution for Free Vibration of Smart Transversely Isotropic Thick Rectangular Plates

In the present research, the free vibration of transversely isotropic thick rectangular plates coupled with surface bounded piezoelectric layers is analyzed analytically. Through-the-thickness variation of electric potential satisfies the Maxwell’s equation as well as open circuit electrical boundary conditions. On the basis of third order shear deformation plate theory, the coupled governing equations are obtained and through using auxiliary functions, reformulated into new decoupled equations. The numerical results for the Levy type of boundary conditions and different plate parameters have been presented. It is found that the effect of piezoelectric layer on the plate natural frequencies highly depends on the plate parameters and the mechanical boundary conditions.

Analytical Solution for Free Vibration of Smart Transversely Isotropic Thick Rectangular Plates Keywords:

Free vibration , Smart transversely isotropic plate , Rectangular plate , Analytical solution , Third order shear deformation plate theory