Parametric Analysis of the Nonlinear Dynamics of a Cracked Cantilever Beam

Abstract Structural damage occurs in a variety of civil, mechanical, and aerospace engineering systems, and it is critical to effectively identify such damage in order to prevent catastrophic failures. When cracks are present in a structure, the breathing phenomenon that occurs between crack surfaces typically triggers nonlinearity in the dynamic response. In this work, in order to thoroughly understand the nonlinear effect of cracks on structural dynamics, two modeling approaches are integrated to investigate the crack-induced nonlinear dynamics of cantilever beams. First, a modeling method referred to as the discrete element (DE) method is employed to construct a model of a cracked beam. The DE model is able to characterize the breathing phenomenon of cracks. Next, a simulation technique referred to as the hybrid symbolic-numeric computational (HSNC) method is used to analyze the nonlinear response of the cracked beam. The HSNC method provides an efficient way to evaluate both stationary and nonstationary dynamics of cracked systems since it combines efficient linear techniques with an optimization tool to capture the system’s nonlinear response. The proposed computational platform thus enables efficient multiparametric analysis of cracked structures. The effects of crack location, crack depth, and excitation frequency on the cantilever beam are parametrically investigated using the proposed method. Nonlinear features such as subharmonic resonance, nonstationary motion, multistability, and frequency shift are also discussed in this paper.