Forced vibration analysis of functionally graded beams by the meshfree boundary-domain integral equation method

Abstract

Forced vibration of two-dimensional functionally graded beams is studied in this paper by a developed meshfree boundary-domain integral equation method. Material properties of the functionally graded beams are assumed varying continuously either in longitudinal or transvers direction following the exponential function. The boundary-domain integral equations are derived by using the elastostatic fundamental solutions based on the two-dimensional elastic theory. Radial integral method (RIM) is employed to transform the domain integrals into boundary integrals. A meshfree scheme is achieved through assuming the displacements and accelerations in the domain integrals by a combination of the radial basis function and polynomials with time dependent coefficients. Wilson-θ, Houbolt as well as two kinds of damped Newmark's algorithms are applied to accomplish the time integration. The forced vibration of the functionally graded beam subjected by the harmonic loading and transient loading are investigated in detail. Numerical examples demonstrate that the four mentioned time integral schemes are all adapted well to the developed meshfree boundary-domain integral equation method for analyzing the forced vibration of homogeneous structures. For the analysis of FG structures, it is shown that the damped Newmark's algorithm can achieve more stable and accurate results.