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

Explicit Analytical Representations in the Multiple High-Frequency Reflection of Acoustic Waves from Curved Surfaces: The Leading Asymptotic Term

In the context of wave propagation through a three-dimensional acoustic medium, we develop an analytical approach to study high-frequency diffraction by multiple reflections from curved surfaces of arbitrary shape. Following a previous paper (of one of us) devoted to two-dimensional problems, we combine some ideas of Kirchhoff’s physical diffraction theory with the use of (multidimensional) asymptotic estimates for the arising diffraction integrals. Some concrete examples of single and double reflection are treated. The explicit formulas obtained by our approach are compared with known results from classical geometrical diffraction (or Ray-) theory, where this is applicable, and their precision is tested by a direct numerical solution of the corresponding diffraction integrals

Some results on the energy transmission through an elastic half-space loaded by a periodic distribution of vibrating punches

Abstract - We develop an analytical approach to study the wave process arising in an elastic half-space because of harmonic vibrations applied on its free surface by a (periodic) distribution of rigid punches. By assuming perfect coupling between punches and halfspace, the (in-plane) propagation problem is firstly reduced to a 2 × 2 system of integral equations for the contact stresses. Then, in the frequency range implying the so-called one-mode (far-field) propagation, suitable mild approximations on the kernels lead to some related auxiliary systems of integral equations, which are independent on frequency and can be solved analytically. The explicit formulas thus obtained are reflected through some figures and enable us to discuss the energetic properties of the wave process with respect to frequency. A direct numerical treatment of the original system of (exact) integral equations confirms the precision of the analytical solution. Keywords: Vibrating punches · Energetic properties of wave propagation · Analytical result

Reconstruction of round voids in the elastic half-space: Antiplane problem

We study the reconstruction of geometry (position and size) of round voids located in the elastic half-space, in frames of antiplane two-dimensional problem. We assume that a known point force is applied to the boundary surface of the half-space, and we can measure the shape of the surface over a certain finite-length interval. Then, if the geometry of the defect is unknown, we construct an algorithm to restore its position and size. Some numerical examples demonstrate a good stability of the proposed algorithm

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

FINANCIAL ASPECTS OF ESTABLISHING THE INSTITUTION OF THE SELF-EMPLOYMENT

The concept of self-employment as a form of individual entrepreneurship has been considered. A detailed analysis of the experience of foreign countries in establishing the institution of the self-employment,common and distinctive features of the applied models of the development of self-employment in European countries, Australia and the USA, has been presented. Much attention has been paid both the characteristic of the category “self-employed citizens” and the review of their areas of activity in Russia today. Available mechanisms and tools for the development of self-employment have been analyzed. Particular attention has been paid to the analysis of the concept of self-employment and its forms, presented in legislative acts, which serve as the basis for effective regulation by the government. Conclusions and recommendations of the authors on the application of the new special tax treatment on the income of self-employed citizens, implemented as part of a pilot project in several regions of the Russian Federation, have been presented