A nonlinear breathing crack model for characterization of chaotic dynamics of damaged large-amplitude vibrating plates

Abstract

Large-amplitude vibrating plates (LVPs) inherently exhibit intricate chaotic behaviors stemming from geometric nonlinearity. Such chaotic dynamics could be substantially influenced by the occurrence of a breathing crack, characterized by a cyclic opening and closing process. However, current models for breathing cracks primarily focus on beam-like structures and often rely on the assumption of periodic dynamical responses, which is inadequate for depicting the chaotic vibrations experienced by cracked LVPs. To that end, this study presents a novel nonlinear breathing crack model (NBCM) to precisely characterize the breathing effect on chaotic dynamics of large-amplitude vibrating plates containing a parallel part-through breathing crack. By refining the line spring model and devising a mathematical expression for crack parameters and dynamical responses, the NBCM-based governing equation for cracked LVPs is derived with a Duffing type expression having a quadratic term. Through the utilization of the harmonic balance method and the Hilbert–Hughes–Taylor algorithm, both analytical and numerical dynamic responses of the cracked LVP based on the NBCM are obtained. Comprehensive nonlinearity analyses are then conducted, including hardening nonlinearity, breathing nonlinearity, and bifurcation nonlinearity. Comparison results demonstrate the superiority of the presented nonlinear breathing crack model in characterizing the chaotic dynamics of LVPs with breathing cracks. Accordingly, the presented NBCM shows significant potential for identifying abnormalities within practical engineering plate-like structures when considering the effects of crack breathing.