scholarly journals Plane contact problem on the interaction of a pre-stressed strip with an infinite inhomogeneous stringer

2020 ◽  
Vol 97 (3) ◽  
pp. 55-63
Author(s):  
N. Dikhtyaruk ◽  
E. Poplavskaya ◽  
Keyword(s):  
Fourier Transform ◽  
Differential Equations ◽  
Theory Of Elasticity ◽  
Contact Stresses ◽  
Algebraic Equations ◽  
Distribution Law ◽  
Linearized Theory Of Elasticity ◽  
Linearized Theory ◽  
The Fourier Transform ◽  
Resolving System

The article is devoted to the study of problems of contact interaction of an infinite elastic inhomogeneous stringer with a prestressed strip clamped along one edge. As a result of the research, we have obtained a resolving system of recurrent systems of integro-differential equations. In general, the studies were carried out for the theory of large initial and various versions of the theory of small initial deformations within the framework of the linearized theory of elasticity with an elastic potential of an arbitrary structure. Integral integer differential equations are obtained using the integral Fourier transform. Their solution is presented in the form of quasiregular infinite systems of algebraic equations. The article also investigates the influence of the initial (residual) stresses in strips on the distribution law of contact stresses along the line of contact with an infinite stringer. The system is solved in a closed form using the Fourier transform. The stress expressions are represented by Fourier integrals with a fairly simple structure. The influence of the initial stress on the distribution of contact stresses has been studied and mechanical effects have been found under the action of concentrated loads.

scholarly journals A flat contact problem the interaction two prestressed stripes with an infinite stringer

2019 ◽  
Vol 24 (94/4) ◽  
pp. 40-48
Author(s):  
N.N. Dikhtyaruk ◽  
E.A. Poplavskaya
Keyword(s):  
Fourier Transform ◽  
Contact Problem ◽  
Theory Of Elasticity ◽  
Contact Stresses ◽  
Algebraic Equations ◽  
Infinite Systems ◽  
Integral Fourier Transform ◽  
Linearized Theory Of Elasticity ◽  
Linearized Theory ◽  
Flat Contact

The article is devoted to the research of problems of contact interaction of infinite elastic stringer with two identical clamped along one edge of pre-stressed strips. In general, the research was carried out for the theory of great initial and different variants of the theory of small initial deformations within the framework of linearized theory of elasticity with the elastic potential having arbitrary structure. The integral integer-differential equations are obtained using the integral Fourier transform. Their solution is represented in the form of quasiregular infinite systems of algebraic equations. In the article alsaw was investigated the influence of the initial (residual) stresses in strips on the law of distribution of contact stresses along the line of contact with an infinite stringer.  The system is solved in a closed forms using transformation of Fourier. Expressions of stresses are represented by Fourier integrals with a simple enough structure. Influence of initial stress on the distribution of contact stresses is study and discovered the mechanical effects under the influence of concentrated loads

scholarly journals Contact interaction of prestressed annular punch and half-space

2020 ◽  
pp. 24-30
Author(s):  
S.Yu. Babich ◽  
◽  
N.O. Yaretska ◽  
Keyword(s):  
Half Space ◽  
Contact Interaction ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Natural State ◽  
Small Perturbations ◽  
Linearized Theory Of Elasticity ◽  
Annular Punch ◽  
Linearized Theory ◽  
Deformed State

The article is devoted to the task of contact interaction of the pressure of a pre-stressed cylindrical annular punch on the half-space with initial (residual) stresses without friction. It is solved for the case of unequal roots of the characteristic equation. In general, the research was carried out for the theory of great initial (ultimate) deformations and two variants of the theory of small initial ones within the framework of linearized theory of elasticity with the elastic potential having any structure. It is assumed that the initial states of the elastic annular stamp and the elastic half-space remain homogeneous and equal. The study is carried out in the coordinates of the initial deformed state, which are interrelated with Lagrange coordinates (natural state). In addition, the influence of the annular stamp causes small perturbations of the basic elastic deformed state. It is assumed that the elastic annular stamp and the elastic half-space are made of different isotropic, transversal-isotropic or composite materials.

scholarly journals Radiation analysis of sound waves from semi-infinite coated pipe

2018 ◽  
Vol 18 (1) ◽  
pp. 92-111 ◽  
Author(s):  
Burhan Tiryakioglu ◽  
Ahmet Demir
Keyword(s):  
Fourier Transform ◽  
Sound Waves ◽  
Algebraic Equations ◽  
Total Field ◽  
Hopf Equation ◽  
Waveguide Modes ◽  
Linear Algebraic Equations ◽  
Pipe Radius ◽  
Expansion Coefficients ◽  
The Fourier Transform

An analytical solution is presented for the problem of radiation of sound waves from a semi-infinite circular cylindrical coated pipe which is partially lined from inside. By stating the total field in duct region in terms of normal waveguide modes (Dini’s series) and using the Fourier transform technique elsewhere, we obtain a Wiener–Hopf equation whose solution involving three sets of infinitely many unknown expansion coefficients satisfying three systems of linear algebraic equations. This system is solved numerically and the influence of some parameters (pipe radius, impedances, extension, etc.) on the radiation phenomenon is displayed graphically.

scholarly journals Dispersion of generalized Rayleigh waves in the half-plane covered with pre-stretched two layers under complete contact

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 247-253
Author(s):  
Muslum Ozisik
Keyword(s):  
Wave Propagation ◽  
Rayleigh Wave ◽  
Half Plane ◽  
Single Layer ◽  
Theory Of Elasticity ◽  
Phase Zone ◽  
Contact Conditions ◽  
Linearized Theory Of Elasticity ◽  
Linearized Theory ◽  
Complete Contact

In this paper the dispersion of the generalized Rayleigh wave propagation in the non-prestressed half-plane covered with pre-stretched two layers under complete contact conditions is investigated by 3-D linearized theory of elasticity. The layers and the half-plane are assumed that elastic, homogeneous, isotropic, and the complete contact conditions are existed. The inter phase zone between the upper layer and half-plane is modeled by this second layer. The purpose of the investigation is the determination on the effect of the existence of the second layer to the considered generalized Rayleigh wave propagation velocity. For this purpose, firstly the same materials were selected for both layers and the results obtained in previous studies for a single layer in the literature were verified, the accuracy of the modeling was shown, and then the effect of the second layer on the considered problem was shown by selecting the different materials and applying different initial pre-stresses. Consequently, the present study can be considered as the investigation of the existence of the inter phase zone which is characteristic one for the composite materials to the dispersion of the generalized Rayleigh wave propagation. Numerical results obtained and discussed.

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