Strain gradient vibration analysis of piezoelectric composite microplate reinforced with FG-GPLs based on sinusoidal shear deformation theory

Here, the basic formulation of nonlocal strain gradient theory (SGT) and sinusoidal shear deformation theory (SSDT) are used to analyze the free vibration behavior of functionally graded graphene nanoplatelets reinforced piezoelectric composite (FG-GPLRPC) microplate. To provide a realistic model based on the Kelvin Voigt model, the material properties of the structure are assumed to be viscoelastic. The viscoelastic FG-GPLRPC microplate is resting on the orthotropic visco Pasternak foundation and is exposed to the electromagnetic field. Four different patterns of functionally graded distributions of GPLs, uniform distribution, and non-uniform distributions such as FG-A, FG-O, and FG-X are considered. The effective Young's modulus, density, and Poisson's ratio of FG-GPLRPC microplate are determined based on the Halpin-Tsai micromechanics model and the mixture rule, respectively. Finally, Hamilton's principle is applied to obtain the equations of motion. The simply supported plate is assumed to study the dimensionless eigenfrequency with the analytical approach. The results are compared with other published papers to show the validity of the proposed approach. It is seen that growing the aspect ratio leads to about 33% increase and decrease in the system frequency for high and low damping coefficient values, respectively.