Reconstruction of Crack Cluster in the Rectangular Domain by Ultrasonic Waves

In the present article we study the reconstruction problem for clusters of linear cracks inside a rectangular domain. The parameters to be reconstructed are the number of cracks and the size and slope of each defect. The scanning is performed by a single ultrasonic transducer placed at a certain boundary point. The input data, used for the reconstruction algorithm, is taken as measured oscillation amplitudes over an array of chosen boundary points. The proposed numerical algorithm is tested on some examples with multiple clusters of cracks whose position and geometry are known a priori

An efficient representation for kernels in the 2d dynamics displacement discontinuity method for cracked elastic materials

The displacement discontinuity method is a rather standard approach to study cracks in elastic materials. This is in fact a certain technique to construct the system of Boundary Integral Equations (BIE), or equivalently, Boundary Element Methods (BEM). In the static case this typically results in explicit expressions for the kernels of respective BIE, both in 2d and 3d problems. In the work the authors give efficient representations for such kernels in explicit form

On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics

In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work is the development of an efficient direct numerical collocation method. The paper is completed with two examples taken from crack theory and acoustics: the study of a single crack in a linear isotropic elastic medium, and diffraction of a plane acoustic wave by a thin rigid screen.Comment: accepted by Acta Mechanica, 19 pages, 3 figure

On multiple crack identification by ultrasonic scanning

The present work develops an approach which reduces operator equations arising in the engineering problems to the problem of minimizing the discrepancy functional. For this minimization, an algorithm of random global search is proposed, which is allied to some genetic algorithms. The efficiency of the method is demonstrated by the solving problem of simultaneous identification of several linear cracks forming an array in an elastic medium by using the circular Ultrasonic scanning

An Efficient Method in 2D problem on Transient Oscillations of the Elastic Half-Space Interacting with a Rigid Structure

Abstract We propose an efficient method to study the (two-dimensional) in-plane nonstationary (transient) problem for a rigid rectangular structure above the oscillating foundation. A massive structure is perfectly coupled with the foundation, whose oscillations are caused by an oblique plane seismic wave incoming from below to the boundary surface. The structure is assumed to be considerably more rigid than the foundation. The mathematical formulation admits application of the Laplace transform over time and Fourier transform along the horizontal coordinate. By satisfying the boundary conditions over the contact zone between the rectangle and the foundation, the problem is reduced to a system of two integral equations for normal and tangential contact stress, which contain the Laplace parameter. To solve this system, we apply a numerical method to arising Volterra`–Fredholm integral equations. Then the dynamic properties of the structure is studied for various combinations of physical and geometrical parameters

Flow-induced vortex field generated by a thin oscillating plate in an aeroacoustics framework

The authors study the structure of the vortex sheet generated by a thin rectangular plate harmonically oscillating in a flow of non-viscous fluid. In frames of the Lighthill-Curle and Powell aeroacoustic theories, it is shown that the shedding vortices determine the magnitude of the generated sound. The problem is reduced to a dual integral equation which is solved numerically. The solution defines the sound of the load, as well as the components of the vortex vector over the sheet. Some examples of the numerical treatment are shown for various combinations of physical parameters

REFLECTION OF PLANE WAVES BY THE FREE BOUNDARY OF A POROUS ELASTIC HALF-SPACE

In the present paper, we studyreflection of inclined incident plane waves from a free boundaryof the half-space in which the material is described byconstitutive equations valid for elastic solids with voids. Both the cases of the transverse and longitudinal incident waves are considered, and it is shown that onlythe transverse one can propagate in the solid without attenuation, after having been reflected from the free boundarysurface. The reflection coefficient and the amplitude of the surface oscillations are expressed in explicit form. The general results are demonstrated for several hypothetical porous materials, and it is shown that the reflection coefficient and the vibration amplitude are typically less than in classical media without voids. However, for relativelylarge transverse wave speed and high porosity, free boundary oscillation can exceed the classical on