Resonant frequencies of the scattering of elastic waves by three-dimensional cracks

et al. 2012

Smart Mater. Struct.

The research aims at an experimental approval of the trapping mode effect theoretically predicted for an elastic plate-like structure with a horizontal crack. The effect is featured by a sharp capture of incident wave energy at certain resonance frequencies with its localization between the crack and plate surfaces in the form of energy vortices yielding long-enduring standing waves. The trapping modes are eigensolutions of the related diffraction problem associated with nearly real complex points of its discrete frequency spectrum. To detect such resonance motion, a laser vibrometer based system has been employed for the acquisition and appropriate visualization of piezoelectrically actuated out-of-plane surface motion of a two-layer aluminum plate with an artificial strip-like delamination. The measurements at resonance and off-resonance frequencies have revealed a time-harmonic oscillation of good quality above the delamination in the resonance case. It lasts for a long time after the scattered waves have left that area. The measured frequency of the trapped standing-wave oscillation is in a good agreement with that predicted using the integral equation based mathematical model.

Section: Introductionmentioning

confidence: 99%

Wave energy trapping and localization in a plate with a delamination

Глушков

Glushkova

et al. 2012

Smart Mater. Struct.

“…In accordance with the integral approach [29], the scattered field can be expressed in terms of the two-dimensional Fourier transform with respect to x 1 , x 2 :…”

Section: Wavefields In a Medium With A Periodic Array Of Interface Cracksmentioning

confidence: 99%

Wave propagation through an interface between dissimilar media with a doubly periodic array of arbitrary shaped planar delaminations

Mathematics and Mechanics of Solids

Doroshenko

2017

This paper considers the scattering of elastic waves by a doubly periodic array of three-dimensional planar delaminations at the interface between two dissimilar media. The delaminations are modelled in terms of the spring boundary conditions, which are employed to formulate a boundary integral equation. The problem is solved using the Bubnov–Galerkin scheme and the integral approach, taking into account geometrical periodicity. The effects of distribution and shape of periodic delaminations on wave transmission and diffraction are analysed. The specific phenomenon of pass-bands or an ‘opening’ interface for wave propagation by a periodic array of delaminations is revealed.

“…The BIEM is efficient for the solution of the scattering problem for strip-like [24][25][26], penny-shaped [24,[27][28][29][30][31][32][33][34][35], elliptic [36], rectangular [37,38] arbitrary shaped [39] cracks. In the 1990s, location of the resonance poles or eigenfrequencies in the complex frequency plane for an elastic space was investigated for circular crack [40], elliptical crack [41] as well as rectangular and L-shaped cracks [38]. Boundary integral equations derived for a crack in a homogeneous space can be uncoupled into two equations, which is not possible for interface cracks between two dissimilar media.…”

Section: Introductionmentioning

confidence: 99%

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

Doroshenko

2021

Mathematics

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.