Dispersion of Longitudinal Waves by Four Coplanar Mode-I Cracks in an Infinite Elastic Medium

Mandal, Palas and Somala, S N and Narayanakumar, S (2021) Dispersion of Longitudinal Waves by Four Coplanar Mode-I Cracks in an Infinite Elastic Medium. International Journal of Applied and Computational Mathematics, 7 (3). ISSN 2349-5103

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Abstract

A study is made of incident P- waves between four coplanar Griffith cracks, which are located symmetrically in the midplane of an infinite elastic medium. A two-dimensional elastic wave equation is considered for an isotropic medium. The Fourier integral transform has been applied to convert the fundamental problem to an integral equation problem. We have utilized the finite Hilbert transform technique and Cook's result to solve five integral equation. This work's main objective is to investigate the dynamic stress intensity factors and crack opening displacement at the cracks' tips. The study of these physical quantities (SIF, COD) predicts possible arrest of the damages within a specific range of wave frequency by monitoring the applied load. For low frequency, we have shown the graphs of SIF and COD for various types of isotropic materials and concluded that crack propagation could arrest quickly within a specific range of frequency. We presented a parametric study to explore the influence of crack growth and propagation.

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