Thermal postbuckled vibrations of symmetrically laminated composite plates with initial geometric imperfections

In the present paper the postbuckling and postbuckled vibrations of symmetrically laminated composite plate subjected to a uniform temperature distribution through the thickness is presented. The structural model is based on a higher-order shear deformation theory incorporating von Kármán nonlinear strain–displacement relations and initial geometric imperfections. Adopting a multi-term Galerkinʹs approximation, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations in the case of postbuckling analysis and nonlinear ordinary differential equations in the case of free vibration analysis. The critical buckling temperatures are obtained from the solution of the corresponding linear eigenvalue problems. Postbuckled equilibrium paths are traced by solving the nonlinear algebraic equations, via the Newton–Raphson iterative procedure. The free vibration frequencies of a thermally postbuckled plate are reported by solving the eigenvalue problem for different postbuckled deflections.