Free Vibration of Functionally Graded Material Beam under Thermal Loads

Abstract

The material properties of FGM beams are assumed to vary continuously through the thickness according to power law distribution. Based on the assumption that plane section remains plane and normal to the beam axis, the differential equations of motion were established for free vibration of FGM elastic beams under thermal loads and mechanical loads on the premise of the middle plane strain caused by heterogeneity of the materials. Natural frequency and dominant mode shape of FGM beams with four kinds of boundary conditions were obtained.