VIBRATION CHARACTERISTICS ANALYSIS OF FUNCTIONALLY GRADED BEAMS WITH INITIAL GEOMETRIC DEFECT

For the vibration problem of a functionally graded beam with initial geometric defect, based on the meso-structure model of functionally graded materials, the power function is used to simulate the variation of material composition along the direction of beam thickness. Based on the Euler-Bernoulli beam theory, the axial strain expression was obtained from the geometric equation and Marguerre strain, the differential equation of motion for the functionally graded beam with initial geometric defect was derived by using the Hamilton principle in the dimensionless form. The dimensionless differential equations of mode and boundary conditions are discretized by differential quadrature method, and the eigen-equation is obtained. Finally, the effects of gradient index, initial geometric curvature, boundary constraints on the dimensionless natural frequency and modes of the beam with initial geometric defects are analyzed.