Forced vibrations of functionally graded annular and circular plates by domain‐boundary element method

Abstract

AbstractAxi‐symmetric dynamic response of functionally graded circular and annular Mindlin plates with through‐the‐thickness variations of physical properties is investigated by a new domain‐boundary element formulation. Three governing partial differential equations of motion of the inhomogeneous plate are converted to integral equations by utilizing the static fundamental solutions of the displacement components. These integral equations are then spatially discretized by dividing the entire domain into a number of cells and incorporating suitable shape functions to approximate the variation of unknown parameters across the cells. The resulting set of ordinary differential equations in time are then solved by the Houbolt method. To verify the accuracy of the developed procedure, dynamic responses generated for a homogeneous plate are compared to those calculated through an analytical solution. Different loading conditions such as step, harmonic, and impulsive loadings are considered for generation of numerical results of dynamic responses of functionally graded circular and annular plates. Convergence characteristics and effects of material inhomogeneity, and geometric parameters are extensively investigated. It has been shown that the presented method is a fast and accurate and technique in elastodynamic analysis of functionally graded plates.