Haar wavelet analysis of axisymmetric vibration of 2-D functionally graded porous thin annular plate resting on the Winkler foundation

Purpose In this paper, free axisymmetric vibration analysis of a two-directional functionally graded porous thin annular plate resting on the Winkler foundation is presented utilizing the classical plate theory (CPT). The mechanical properties are considered to be varying in the radial-thickness plane. Design/methodology/approach Based on the CPT, the governing differential equation of motion is derived. The highest-order derivative of displacement is approximated by Haar wavelets and successive lower-order derivatives are obtained by integration. The integration coefficients are calculated using boundary conditions. The fundamental frequency for clamped-clamped, clamped-simply supported, simply supported-clamped and simply supported-simply supported boundary conditions is obtained. Findings The effects of the porosity coefficient, the coefficient of radial variation, the exponent of power law, the foundation parameter, the aspect ratio and boundary conditions are investigated on fundamental frequency. A convergence study is conducted to validate the present analysis. The accuracy and reliability of the Haar wavelets are shown by comparing frequencies with those available in the literature. Three-dimensional mode shapes in the fundamental mode for all four boundary conditions are presented. Originality/value Based on the Haar wavelet method, a free axisymmetric vibration model of a porous thin annular plate is solved in which 2-D variation of mechanical properties is considered.