Dynamic Response of Shear Deformable Functionally Graded Porous Beams

Abstract

This paper analyzes the dynamic response of a shear deformable functionally graded porous beam under a point harmonic load. Timoshenko beam theory is employed to include the effect of transverse shear strain. The elasticity moduli and mass density of the porous beam vary continuously in the thickness direction based on two different porosity distributions. The relationship between porosity and density coefficients are determined according to the mechanical property of an open-cell metal foam. The equations of motion are derived and solved by applying Ritz method in the space domain and Newmark-β method in the time domain. The dynamic deflections are obtained for porous beams with different boundary conditions. A detailed numerical analysis is presented to show the effects of porosity coefficient and slenderness ratio on the dynamic response of porous beams. The influence of porosity distribution pattern is highlighted to shed a useful insight into the design of functionally graded porous structures.