Abstract
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.
Highlights
The aim of the present paper is mathematical modeling of a pre-fracture state of the construction unit representing the junction of angular elastic elements
It is investigated correctness problems of applying mathematical modeling method for the wave process arising in angular elements examined by non-destructive testing methods both in hard industry enterprises and in ones of agricultural machinery
In its neighborhood there arises the defect growing to the angular point and generating the acoustic radiation
Summary
The aim of the present paper is mathematical modeling of a pre-fracture state of the construction unit representing the junction of angular elastic elements. 1. The boundary value problem is formulated for the dynamic elasticity equations in the domain , presenting the angle of span with cut , simulating the defect located on the segment , of the line . Under the steady oscillations there states the problem of finding the unknown contact stresses in the zone of the contact interaction with the punch, stress saltus on the cut and the reconstructing displacement field in the whole domain including the upper boundary .
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