Nonlinear vibration of a coating-FGM-substrate cylindrical panel subjected to a temperature gradient

This paper deals with the linear and nonlinear vibration analysis of a three-layer coating-FGM-substrate cylindrical panel with general boundary conditions and subjected to a temperature gradient across the thickness due to steady heat conduction. The theoretical formulation is based on geometric nonlinearity in von-Karman sense and the first order shear deformation theory which accounts for the effects of transverse shear strains and rotary inertia. A nonlinear pre-vibration analysis is conducted to determine the thermally induced deformation and pre-stress state of the cylindrical panel due to the bending and stretching coupling effect being introduced by the graded layer. The nonlinear governing differential equations of motion are obtained by adding an incremental dynamic state to the pre-vibration state. A numerical method that makes use of differential quadrature approximation together with iterative algorithms is employed to model the linear and nonlinear vibration behavior of the cylindrical panels. Numerical results are presented in both tabular and graphical forms, showing that the linear and nonlinear vibration frequencies are significantly influenced by vibration amplitude, temperature change, out-of-plane boundary support and the values of a/b, a/h and R/a. The effects of the in-plane displacement constraints and the volume fraction index of the intermediate FGM thin layer are not very prominent.