Vibration characteristics of sandwich plates with GPLRC core and piezoelectric face sheets with various electrical and mechanical boundary conditions

An analysis is performed in the current investigation to study the vibrations of composite laminated plates integrated with piezoelectric layers. Composite laminated plate is reinforced with graphene platelets (GPLs). Also the amount of GPLs in the layers may be different which results in a piecewise functionally graded (FG) media. Elasticity modulus of the GPLRC media is obtained by means of the Halpin-Tsai rule which contains efficiency parameters to capture the size of reinforcements. First order shear deformation theory of plates and parabolic distribution of electric field through the piezoelectric layers are assumed as the basic assumption. For the piezoelectric layers, both the open circuit and closed circuit conditions are applied. The total strain and kinetic energies of the plate are obtained. After that by means of the general idea of the Ritz method and also Chebyshev polynomials as the basic shape functions, the matrix representation of the equations of motion dealing with free vibration of sandwich plate with piezoelectric face sheets are obtained. Results of this study are first compared with the available data in the open literature. After that novel results are given to explore the effects of different parameters such as the electrical and mechanical boundary conditions, plate geometry, GPL weight fraction and GPL distribution profile. It is shown that with introduction of GPLs, frequencies of the plate may be enhanced for both closed circuit and open circuit conditions.