Linear and nonlinear free and forced vibrations of graphene reinforced piezoelectric composite plate under external voltage excitation

Graphene reinforcements can obviously enhance the piezoelectric properties as well as the mechanical properties of the polyvinylidene fluoride (PVDF). This paper investigates the linear and nonlinear vibration behaviors of the smart piezoelectric composite plate reinforced by uniformly and non-uniformly dispersing graphene platelets (GPLs). The effective Young's modulus is predicted by the Halpin Tsai's parallel model while the effective mass density, Possion's ratio and piezoelectric properties are calculated by the rule of the mixture. Based on the first-order shear deformation plate theory, von Karman nonlinear geometric relationship and Hamilton's principle, the governing equations of motion under different boundary conditions are derived for the smart piezoelectric composite plate. The governing equations of motion are solved to obtain the nonlinear eigenvalue equations by the differential quadrature (DQ) method. The analysis is validated by comparing with the current results of the smart piezoelectric composite plate. The effects of the GPL distribution pattern, stratification number, concentration and geometry of GPLs, plate geometry, external voltage and piezoelectric properties of GPLs as well as boundary conditions on the linear and nonlinear vibration behaviors are discussed in detail. The numerical results clearly illustrate that there exists the great potential for using GPLs in achieving smart structures with significantly improved structural stiffness.