Large Amplitude Free Vibration Analysis of Axially Functionally Graded Plates

Large amplitude free vibration problem of axially functionally graded plates under the action of uniformly distributed load is analyzed using energy method. A variational approach has been applied for the generation of governing differential equations. A two part solution procedure has been adopted, where the static solution is sought in the first part and the dynamic problem is taken up subsequently as a standard Eigen-value problem. The governing differential equations for the static analysis are derived from the principle of minimum total potential energy whereas Hamilton’s principle is used for developing the governing equations for the dynamic analysis. Start functions for the analysis are chosen by satisfying the flexural and membrane boundary conditions and Gram-Schmidt orthogonalization procedure is used for developing the higher order functions. The dynamic behavior is presented as backbone curves in non-dimensional frequency amplitude plane. Mode shape plots for linear and non-linear frequencies are given to show the effect of vibration amplitude on dynamic behavior. The results are compared with the works of other researchers which confirms the accuracy of the present research work.