Axisymmetric bending and flexural vibration analysis of heterogeneous (FGM) circular plates

In this research, an effective numerical approach is applied to the axisymmetric bending and flexural vibration analysis of two-directional functionally graded (2D-FG) thick circular and annular plates with variable thickness. The material properties are assumed to vary continuously both in thickness and radial directions. The effect of shear deformation is considered in the formulation. The governing equations are converted to a set of ordinary differential equations (ODEs). Obtained canonical equations are solved numerically by the Complementary Functions Method (CFM). For the dynamic analysis, the CFM is combined with the Laplace transform. A powerful inverse algorithm is applied to retransfer the results from the Laplace space to the time domain. The damping model of Kelvin is used in the damped forced vibration analysis. The main purpose is to infuse this method to the bending and dynamic analysis of a wide range of solid circular or annular plates, with linear or non-linear thickness profiles, radially Functionally Graded (FG), FG in the thickness direction or 2D-FG, without any restrictions. The influence of material variation exponents and thickness profiles on the considered problems are investigated. Several examples are presented and results are verified with those obtained by finite element method and available published literature. Excellent agreement is observed.