Analysis of Eigenfrequencies of a Circular Interface Delamination in Elastic Media Based on the Boundary Integral Equation Method

Mikhail V. Golub and Olga V. Doroshenko
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Mikhail V. Golub: Institute for Mathematics, Mechanics and Informatics, Kuban State University, 350040 Krasnodar, Russia
Olga V. Doroshenko: Institute for Mathematics, Mechanics and Informatics, Kuban State University, 350040 Krasnodar, Russia

Mathematics, 2021, vol. 10, issue 1, 1-20

Abstract: The widespread of composite structures demands efficient numerical methods for the simulation dynamic behaviour of elastic laminates with interface delaminations with interacting faces. An advanced boundary integral equation method employing the Hankel transform of Green’s matrices is proposed for modelling wave scattering and analysis of the eigenfrequencies of interface circular partially closed delaminations between dissimilar media. A more general case of partially closed circular delamination is introduced using the spring boundary conditions with non-uniform spring stiffness distribution. The unknown crack opening displacement is expanded as Fourier series with respect to the angular coordinate and in terms of associated Legendre polynomials of the first kind via the radial coordinate. The problem is decomposed into a system of boundary integral equations and solved using the Bubnov-Galerkin method. The boundary integral equation method is compared with the meshless method and the published works for a homogeneous space with a circular open crack. The results of the numerical analysis showing the efficiency and the convergence of the method are demonstrated. The proposed method might be useful for damage identification employing the information on the eigenfrequencies estimated experimentally. Also, it can be extended for multi-layered composites with imperfect contact between sub-layers and multiple circular delaminations.

Keywords: elastic waves; boundary integral equation method; spring boundary conditions; laminate; delamination; eigenfrequency; diffraction; damage; resonance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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