Nonlinear vibrations of a beam with a breathing edge crack

Abstract

In this paper, nonlinear transverse vibration analysis of a beam with a single edge crack is studied. In literature, edge cracks are generally modeled as open cracks, in which the beam is separated into two pieces at the crack location and these pieces are connected to each other with a rotational spring to represent the effect of crack. The open edge crack model is a widely used assumption; however, it does not consider the nonlinear behavior due to opening and closing of the crack region. In this paper, a beam like structure with a breathing type crack is studied. Due to the breathing nature of the crack, crack surfaces contact with each other for some period of the motion and separate in the rest of the cycle. This nonlinear behavior of the crack region is modeled by representing the system as a single degree of freedom system (SDOF) with a bilinear stiffness by Galerkin’s Method. Nonlinear differential equations of motion obtained by using Euler-Bernoulli beam theory are converted into nonlinear algebraic equations by using harmonic balance method (HBM). Under the action of a harmonic forcing, the effect of crack parameters on the vibrational behavior of the cracked beam is presented.