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.
Highlights
Widespread occurrence of composite structures in aerospace, aircraft, geophysics, building construction as well as in high-performance products led to the growth of the studies of the dynamics of various inhomogeneities or defects
The present paper demonstrates that the proposed boundary integral equations method (BIEM) is an efficient tool for the eigenfrequencies calculation and classification
The proposed advanced BIEM is more efficient for eigenfrequencies calculation than the meshless method and the finite element method, which demand more computational costs for the system composition and solution as well as eigenfrequencies determination
Summary
Crack analysis became a natural task for engineering applications due to the importance of the detection of defects and flaws known as delaminations. The determination of the wave resonances and the eigenfrequencies or the natural frequencies has wide applications such as acoustic spectroscopy, prediction of possible structural failure and non-destructive testing. Wave propagation at the resonance frequencies exhibits itself in the larger resulting wave amplitudes and wave localization, which can be employed for determining the shape and properties of inhomogeneities using electromagnetic and acoustic waves [1]. Local defect resonances were employed in the matters of non-destructive testing. Inverse problems of the crack identification based on natural frequencies were studied theoretically and experimentally for rods [2,3] and plates [4,5]
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