Imperfection sensitivity of nonlinear primary resonance behavior in bi-directional functionally graded porous material beam

Abstract

This research aims to analyze the imperfection sensitivity in the nonlinear resonance behavior of bi-directional functionally graded (BDFG) porous beam. The trigonometric and hyperbolic functions are chosen to describe the global and localized geometrical imperfections. Considering the first-order shear deformation theory and von-Kármán’s geometric nonlinearity, theoretical model is formulated to depict the coupled motion including the stretching, bending and shear deformations of BDFG porous beam. Differential quadrature based Galerkin’s procedure is proposed to formulate the reduced model. The nonlinear responses are obtained by using the numerical bifurcation method. Numerical results demonstrate that resonance response of beam under goes cyclic-fold bifurcations. Resonance behavior of beam may exhibit hardening, softening or softening-hardening type nonlinearity. Imperfection sensitivity analysis shows that the variation of imperfection modes, material gradient and porosity change the characteristic of frequency-response and force-response or even the number of bifurcation points. .