Crack-induced guided wave motion and modal excitability in plates using elastodynamic reciprocity

Abstract

This paper presents solutions and comparisons for guided wave motion (Lamb and shear horizontal) due to tensile and shear cracks in an isotropic plate using elastodynamic reciprocity. Cracks are treated as point sources, which for the ease of wave motion analysis have equivalent body force representations. The paper then outlines the use of elastodynamic reciprocity for obtaining the wave motion due to equivalent body forces for tensile (Mode I) and shear (Mode II or III) cracks. A far-field analysis is subsequently performed in order to simplify the results and facilitate a direct comparison of guided mode excitability due to the three cracking modes. A parametric study in an aluminum plate is carried out for the dependence of guided mode excitability on frequency, crack depth, and propagation direction. The study reveals the intricate frequency and depth dependence of the excitability for various fundamental and higher-order modes. Although tensile cracking exhibits complex Lamb mode radiation patterns, a simple and universal closed-form expression is derived for the low-frequency limit (<0.5 MHz-mm). Afterward, the analysis is validated against a 3D FEM model, confirming the predictions of the theory.