Open AccessFine elastic circular inclusion in the area of harmonic vibrations of an unlimited body under smooth contact
Author(s) -
Larisa Vakhonina,
Natalya Potryvaieva,
О. Sadovyi
Publication year - 2020
Publication title -
vìsnik agrarnoï nauki pričornomor'â
Language(s) - English
Resource type - Journals
eISSN - 2411-9199
pISSN - 2313-092X
DOI - 10.31521/2313-092x/2020-4(108)-11
Subject(s) - isotropy , harmonic , vibration , mathematical analysis , matrix (chemical analysis) , integral equation , fredholm integral equation , mathematics , singular integral , stress (linguistics) , displacement (psychology) , geometry , mechanics , classical mechanics , physics , materials science , optics , acoustics , composite material , linguistics , philosophy , psychology , psychotherapist
Fine elastic circular inclusion in the area of harmonic vibrations of an unlimited body under smooth contact The problem of the interaction of harmonic waves with a thin elastic circular inclusion, which is located in an elastic isotropic body (matrix), is solved. On both sides of the inclusion between it and the body (matrix), the conditions of smooth contact are realized. The solution method is based on representing the displacements in the matrix through discontinuous solutions of the Lamé equations for harmonic vibrations. This made it possible to reduce the problem to Fredholm integral equations of the second kind with respect to functions associated with jumps in normal stress and radial displacement to included ones. After the realization of the boundary conditions on the sides of the inclusion, a system of singular integral equations is obtained to determine these jumps. Keywords: elastic inclusions, cylindrical waves, matrix, stress intensity factor.