Dynamic analysis of axisymmetric heterogeneous plates via finite element method in the laplace domain

The main purpose of this thesis is to theoretically examine the static and forced vibration of Functionally Graded Material (FGM) axisymmetric plates. The material properties are assumed to be isotropic, linear viscoelastic or elastic and vary continuously in the direction of the thickness of the plate. In the bending case, Functionally Graded Porous (FGP) materials are used, while in the dynamic case, FGM are used throughout the thickness. For the static state, three different porosity distributions (uniform, symmetric and monolithic) are used. The effect of porosity on the axisymmetric bending analysis of circular plates is analyzed parametrically. In many engineering applications clamped, roller, simply supported types, which are widely used to ensure ideal boundary conditions, have been applied. In the dynamic analysis, the equation governing the event is obtained in Laplace domain with the help of the Laplace transformation, depending on a number of Laplace parameters and independent of time. A modified Durbin's inverse Laplace method is used to move from Laplace domain to time domain. Forced vibration behavior is considered for six periods. 64, 128 and 512 time steps are used in the solutions and the results obtained for these steps are compared. As a result of the comparison, it is revealed that 64 time steps are sufficient for six periods. This effective feature of the method used significantly facilitates the working process in terms of time and effort. The first uniqueness of this research is that it is the first time that the static behavior of functionally graded porous FGP plates is addressed with the Finite Element Method (FEM) using quadrilateral elements. According to the results obtained from the static analysis, it has seen that the displacement of the plate increased as the porosity coefficient and the ratio of the thickness of the circular plates to their radius increased. As the porosity coefficient increased, the displacement values of plates with uniform porosity distribution are affected more than those with symmetrical and monolithic porosity distributions. To model the circular and annular plates, an eight-node quadratic quadrilateral element with two degrees of freedom at each node is implemented. The second originality of this thesis is that the damped and undamped forced vibration behavior of (FGM) axisymmetric plates is discussed for the first time in Laplace domain with FEM. In dynamic analysis, step load, square wave, sawtooth types etc. Time dependent loads such as are applied. Kelvin damping model is used to examine viscoelastic behavior. The results of this study are confirmed by the published literature and the results of the SEY package program (ANSYS). A good agreement is has been observed between the results of the presented model and the results of different methods. According to the comparisons, it has been shown that the proposed method is extremely accurate and effective. FDM coefficient of variation significantly affects the dynamic behavior of the plates considered. As the material change coefficient increases, displacement amplitudes decrease and periods increase. In the viscoelastic case, it is seen that the amplitudes are damped more quickly as the damping ratio increases. Beating phenomenon has been observed when wave type loads are applied. In this case, it is observed that when the damping coefficient increased, the amplitudes became smaller and approached each other.