ANALYTICAL SOLUTIONS FOR VIBRATION NEAR THE BUCKLED CONFIGURATION OF FGM BEAMS UNDER AN IN-PLANE THERMAL LOADING

摘要

Analytical solution is obtained for the dynamic responses around the buckled configuration of FGM beams subjected to a uniform in-plane thermal loading. The equations governing the axial and transverse deformations of FGM beams are derived based on the classical beam theory and the physical neutral surface concept. The two equations are reduced to a single nonlinear fourth-order integraldifferential equation governing the transverse deformation.By assuming that the amplitude of beam's vibration is infinitesimal,and its response harmonic, the non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations;one for postbuckling and the other for linear vibrations of the beam superimposed upon the buckled configuration. The nonlinear equation is directly solved and analytical solutions for static and dynamic responses are obtained.