Frequency and Buckling Analysis of FG Beams with Asymmetric Material Distribution and Thermal Effect

The frequency and buckling characteristics of functional gradient (FG) beams with asymmetric material distribution in the temperature field are analyzed in this paper. Generally, the asymmetrical material distribution of FG beams results in a non-zero neutral axis and non-zero thermal moment. However, some previous studies adopted the treatment of homogeneous beams in which the neutral axis and thermal moment were set as zero. To this end, a comprehensive FG beam model with thermal effect is developed based on the absolute nodal coordinate formulation, in which Euler–Bernoulli beam theory, Lagrangian strain, exact curvature, thermally induced strain, and neutral axis position are considered. For the convenience of comparisons, the presented model can be simplified into three models which do not consider the neutral axis or thermal moment. The numerical results indicate that the influence of the neutral axis on the thermal axial force is minimal while that on the thermal moment is significant. In the case of the high temperature difference, frequency, critical temperature difference, unstable state, and the buckling type of the FG beams are misjudged when the neutral axis or thermal moment is ignored.