Transient analysis of functionally graded axisymmetric plates via finite element method in the Laplace domain

The principal goal of this research article is to examine the forced vibration of Functionally Graded Material (FGM) axisymmetric plates with the aid of the finite element method in the Laplace space. The material properties are assumed to be isotropic, linear viscoelastic, or elastic and vary continuously in the direction of the thickness of the plate. The governing equations of motion are transferred to the Laplace domain and solved for a set of Laplace parameters. Then, a modified Durbin's inverse Laplace method is employed to retransfer the obtained results back to the time domain. A convergence analysis is conducted to optimize the number of Laplace parameters and time steps. An 8-node quadratic quadrilateral element featuring two degrees of freedom per node is employed to generate the model of the axisymmetric plates. Different loads such as step load, square wave, and sawtooth wave loads are used to observe the impact of load type on the transient response of FGM plates. In viscoelastic analysis, the Kelvin damping model is preferred, and the effect of the damping ratio is investigated. The obtained results are validated with the aid of the available literature and the accuracy of the suggested model is confirmed. It is carried out that the material variation significantly affects the dynamic behavior of the plates, for instance as the material coefficient increases, displacement amplitudes decrease, and periods increase. The novelty of this paper is the employment of the finite element method together with Laplace transformation for addressing the present class of problems for the first time.