Wave propagation in edge cracked functionally graded beams under impact force

Abstract

Wave propagation in an edge cracked cantilever beam composed of functionally graded material (FGM) under the effect of an impact force is studied in this paper. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. Material properties of the beam change in the thickness direction according to exponential distributions. The Kelvin–Voigt model for the material of the beam is used. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. The considered problem is investigated within the Bernoulli-Euler beam theory by using an energy-based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using the Newmark average acceleration method. In the study, the effects of the location of the crack, the depth of the crack and different material distributions on the wave propagations of the FGM beams are investigated in detail.