On the static deformation and frequency analysis of functionally graded porous circular beams

Abstract

Due to the availability of limited literature on functionally graded porous circular beams, the static deformation and free vibration analysis of simply supported functionally graded porous circular beams considering the effects of even and uneven porosities are presented in this paper. The Navier type closed-form solutions are obtained for both static and vibration problems within the framework of the higher-order hyperbolic circular beam theory. The theory considers the effects of transverse shear deformation and rotary inertia. The theory satisfies the transverse shear-stress free boundary conditions at the upper and lower surfaces of the beam. The circular beam is made up of the functionally graded material in which material characteristics vary across the thickness direction using the power-law technique which has been adjusted to approximate the porosity effects with even and uneven distributions. A dynamic version of the virtual work principle is employed to derive the governing differential equations of motion, which are then solved analytically using the Navier solution technique. The non-dimensional values of displacements, stresses, and fundamental frequencies are presented for various values of the power-law index (pi), the radius of curvature (R), porosity volume fraction (α), and type of porosity distribution (even and uneven). The present results are compared in few problems with existing literature and found in good agreement with those. This study also highlights some new results for the reference of future researchers, especially on circular beams.