Vibration and wave propagation in functionally graded beams with inclined cracks

Abstract

This paper proposes an FEA method to study the vibration and wave propagation in functionally graded material (FGM) beams with multiple inclined cracks by introducing the local flexibility matrix caused by the cracks. The bending and tensile stiffnesses of the inclined cracks and their interaction are taken into consideration. Two-node (three degrees of freedom per node) beam element is used. The inclined cracks are equivalent to transversal cracks to calculate the additional flexibility matrix of the inclined cracked FGM beam element. The material properties of the FGM beam are supposed to satisfy the exponential law along its thickness. The governing equations of motion for the FGM beam with multiple inclined cracks are deduced in the frame of Euler-Bernoulli theory and Lagrange function, and numerically solved by the Newmark average acceleration method. Both theoretical and numerical comparisons are presented to validate the present method for the inclined cracked FGM beam with varying boundary conditions, arbitrary inclined crack angles as well as varying inclined crack lengths. The effects of the location, length, inclined angle and number of the inclined cracks as well as material property ratio on the fundamental frequencies and wave propagation characteristics of the inclined cracked cantilever FGM beams are comprehensively investigated.