Vibration of circular functionally graded piezoelectric plates in pre-/postbuckled configurations of bifurcation/limit load buckling

Free vibration of pre-/postbuckled circular functionally graded piezoelectric (FGP) plates is studied in this research. The buckled configurations are considered to be resulting from either thermoelectrical bifurcation buckling or limit load buckling due to lateral loading of thermally preloaded plates. The nonlinear governing equations of motion and associated boundary conditions are extracted by the generalized form of Hamilton's principle. The Ritz finite element method is then implemented to construct the matrix representation of governing equations which are solved by two different strategies including Newton-Raphson scheme and cylindrical arc-length method. The thermoelectromechanical properties of FGPM plates are considered to be graded in the thickness direction on the basis of a power law function. Moreover, two cases of thermal loading, i.e., uniform temperature rise and heat conduction across the thickness as well as two types of boundary conditions, including clamped and simply supported, are considered. Comparison studies are presented to validate the numerical results. Furthermore, extensive parametric studies are conducted to assess the influence of involved parameters.