On a mathematical model in estimating the reliability of technological equipment by non-destructive testing

The mathematical model to describe the acoustic emission (AE) in a massive elastic body by radiating piecewise linear defect at the stage of its extension is considered. Problems of reconstructing the wave field in the body and analyzing characteristics of the defect by AE testing are discussed. The problem in question is reduced to the investigation of a boundary integral equations system. The model presented allows to raise the reliability of non-destructive testing results when estimating the exhaustible resource of equipment under long exploitation as one of the directions to solve the problem of energy saving and efficiency

On a Method in Dynamic Elasticity Problems for Heterogeneous Wedge-Shaped Medium

The method of analysis of steady oscillations arising in the piecewise homogeneous wedge-shaped medium composed by two homogeneous elastic wedges with different mechanical and geometric characteristics is presented. Method is based on the distributions’ integral transform technique and allows reconstructing the wave field in the whole medium by displacement oscillations given in the domain on the boundary of the medium. The problem in question is reduced to a boundary integral equation (BIA). Solvability problems of the BIA are examined and the structure of its solution is established

On a mathematical model of dynamics of the elastic wedge-shaped medium with radiating defect

In the paper the mixed boundary value problem of antiplane vibrations is considered in the elastic wedge-shaped medium containing the radiating defect J2. Radiating generators are assumed to be located on defect boundaries and on the interval J1 of the wedge free boundary as well. The problem of reconstructing the wave field in the whole wedgeshaped region with its boundary is stated. A number of problems of analyzing acoustic emission signals by radiating defect are reduced to the problem considered in connections with using non-destructive testing elements of the technological equipment under exploitation. The problem in question is reduced to studying the solvability problems of the equivalent boundary integral equation system both for stress saltus on the defect J2and contact stresses on the interval J1 of the upper plane of the wedge