On the dispersion relations for a hollow cylinder within inhomogeneous residual stress field

Authors

  • Vatulyan A.O. Southern Federal University, Rostov-on-Don, Российская Федерация
  • Yurov V.O. Southern Federal University, Rostov-on-Don, Российская Федерация

UDC

539.3

Abstract

Identification of residual stresses is one of the most important technical problems allowing estimating correctly a resource of designs. Nowadays there are several ways to estimate the level of residual stress state, among them the most economic and simple one is the acoustic method connected with the measurement of velocities of elastic waves. The waves in the hollow elastic inhomogeneous cylinder with free boundary are considered in the presence of fields of residual stress of various structure (inflating, stretching, torsion). The defining relation of problems on deformation of elastic bodies with residual stresses is nonlinear; the linearized Trefftz model is used. The structure of dispersive multiplicity of a problem is studied. The analysis of standing waves has allowed to establish, that for any laws of change of residual stresses exists three set of the dispersive curves, differing movement kinematics. Fields of an abnormal dispersion are found. Some features of a structure of dispersive curves are revealed, influence on them of type of residual stresses is investigated. On the basis of a method of disturbances the formulas characterizing linear sites of dispersive curves and the formula, reflecting change of a dispersive picture in a vicinity of resonances of various type are received. The numerical and analytical research, allowed to establish degree of influence of type residual stresses and its amplitudes on structure a component of dispersive set and change of velocities of extending modes is carried out.

Keywords:

residual stresses, waves, inhomogeneous cylinder, dispersion relations, asymptotic analysis

Acknowledgement

Работа выполнена при поддержке гранта РФФИ (13-01-00196-а).

Author Infos

Aleksandr O. Vatulyan

д-р физ.-мат. наук, профессор кафедры теории упругости Института математики, механики и компьютерных наук Южного федерального университета, зав. отделом Южного математического института Владикавказского научного центра РАН

e-mail: vatulyan@math.rsu.ru

Viktor O. Yurov

студент Института математики, механики и компьютерных наук Южного федерального университета

e-mail: vitja.jurov@yandex.ru

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Issue

2015. No. 2

Pages

22-29

Submitted

2015-05-08

Published

2015-06-25

How to Cite

Vatulyan A.O., Yurov V.O. On the dispersion relations for a hollow cylinder within inhomogeneous residual stress field. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2015, no. 2, pp. 22-29. (In Russian)

Copyright (c) 2015 Vatulyan A.O., Yurov V.O.

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