Parviz Malekzadeh

In this paper, a transformed differential quadrature method (TDQM) for the free vibration analysis of functionally graded (FG) multilayer nanocomposite eccentric annular plates reinforced by graphene nanoplatelets (GPLs) and embedded in piezoelectric layers is developed. In this regards, a suitable conformal mapping is utilized to calculate the transformed weighting coefficients of the differential quadrature method (DQM) in physical domain which enables one to directly discretize the partial differential equations in the reference domain. The modified Halpin–Tsai model is employed to estimate the effective mechanical properties of the nanocomposites. The governing equations are derived based on the first-order shear deformation theory (FSDT) using Hamilton’s principle and Maxwell’s equation. The numerical results show that the TDQM has a very good convergence rate. Furthermore, the accuracy and reliability of the proposed method are verified by comparing the results with those obtained by simulating some problems via ABAQUS software and also, in the limit cases with those available in the literature. The effects of GPLs weight fractions, number of GPLs reinforced layers, distribution types of GPLs, different boundary conditions and various plate geometrical parameters such as the plate thickness, piezoelectric layers thickness, external electrical voltage and off-set parameter on the natural frequency parameters are investigated.