Effect of porosity and profile axial loading on elastic buckling and free vibration of functionally graded porous beam.

Abstract

Elastic buckling and free vibration behaviour of porous functionally graded beam under profile axial mechanical loading is presented analytically. Symmetric and asymmetric porosity distribution with non linear material functional grading is presented. Buckling study is carried out first, then free vibration study under buckling loads is presented with profile loading. The effect of porosity, porosity pattern, slenderness ratio, boundary condition on critical buckling load and fundamental frequency is also studied. Ritz method with shear and normal deformable beam theory (SNDBT) is employed for formulation. It is observed that, with increase in porosity, buckling load decreases for both porosity distribution whereas, fundamental frequency increases for symmetric porosity distribution and is vice versa for asymmetric porosity distribution under all loading conditions.