Frequency Response of an Impacting Lap Joint

Damage or failure of a relatively small component can precipitate the failure of a larger part of a structure. The behavior of damaged or worn joints is of particular concern. To address contact/impact in structural systems, this work models a structural lap joint from first principles. A beam with four stops and gaps is used to simulate a loose or damaged lap joint, which also represents designed manufacturing clearances in mechanical systems. The goal is to generate frequency responses to identify the local shock effect due to impact. Spatial and temporal solutions are presented for an example case. Converged time histories were used to generate the impulse as a metric of frequency response. Facilitating mode contribution calculations, the metric of impulse proves to be an excellent indicator of complexities in the beam's motion due to excitation frequency. Noncontact regions, sticking motions, local extrema, grazing impacts, and aperiodicities are identifiable for specific operating parameters. These conditions indicate when harmful impact may occur that can ultimately cause local damage within a structure. Knowledge of dangerous operating conditions can better focus on inspection before propagation occurs. 1. Introduction Damage or failure of a relatively small component can precipitate the failure of a larger part of a structure. Even the failure of a single connection can cause overload on other structural members, which may consequently fail. Thus, the behavior of damaged or worn joints is of particular concern. In addition to worn parts, many engineering systems with design/manufacturing clearances lead to nonlinearity and contact. The dynamics of loose joints involve nonlinear support conditions and contact/impact phenomena. Many studies have been performed to model contact/impact, and Gilardi and Sharf [1] provided a good review of different methodologies. Moon and Shaw [2] used a digital simulation of a single mode mathematical model of a cantilever elastic beam impacting a stop at one end. The Runge-Kutta algorithm along with finite difference method was used to provide the integration of bilinear spring equations, which show chaotic vibrations that are qualitatively similar to experimental observations. Shaw [3] considered an elastic beam with a one-sided amplitude constraint subjected to periodic excitation. Experimental results were compared with those given by a theoretical model based upon a single mode analysis of [2]. With just a single mode, the model predicted multiple subharmonic resonances, period doublings, and some chaotic