Vibration and post-buckling of a functionally graded beam subjected to non-conservative forces

Abstract

Vibration and post-buckling of beams made from functionally graded materials (FGM) subjected to uniformly and tangentially compressing follower forces are studied in this paper. Based on the accurately and geometrically nonlinear theory for extensible beams, the dynamic governing equations for FGM beams under non-conservative load are formulated. By using a shooting method to solve the non-linearly differential equations numerically, the responses of post-buckling and free vibration in the vicinity of post-buckling configuration are obtained, in which the hinged-fixed boundary conditions of beam are considered. Effects of material gradient parameter on the critical buckling, post-buckling and lower frequencies of the FGM beam are discussed in details.