Diffraction of Surface Harmonic Viscoelastic Waves on a Multilayer Cylinder with a Liquid

Safarov Ismoil Ibrohimovich,Teshayev Muhsin Khudoyberdiyevich,Kulmuratov Nurillo Rakhimovich,Kuldashov Nasriddin Urinovich

doi:10.4236/am.2019.106033

Abstract

An infinitely long circular cylinder, consisting generally of a finite number of coaxial viscoelastic layers, surrounded by a deformable medium is considered. The dynamic stress—the deformed state of a piecewise-homogeneous cylindrical layer from a harmonic wave is investigated. The numerical results of stress, depending on the wavelength are obtained.

Highlights

Modern underground pipelines operate under conditions of static and dynamic loads, which are accompanied by large damage and even failure of the whole system [1]-[6]
In the case of a sufficiently long cavity, the impact perpendicular to its longitudinal axis, the environment surrounding the cavity and the lining are in conditions of plane deformation, and the task of determining the stress state of the array and lining reduces to a flat problem of the dynamic theory of elasticity [7]
The problem is solved in displacement potentials, for this we present the displacement vector in the form: uj = grad (φ j ) + rot (ψ j ), ( j = 1, 2, N )

Summary

Introduction

Open AccessDuring seismic impacts, modern underground pipelines operate under conditions of static and dynamic loads, which are accompanied by large damage and even failure of the whole system [1]-[6]. In the case of a sufficiently long cavity, the impact perpendicular to its longitudinal axis, the environment surrounding the cavity and the lining are in conditions of plane deformation, and the task of determining the stress state of the array and lining reduces to a flat problem of the dynamic theory of elasticity (and whether visco-elasticity) [7]. In [11], the problem of stress concentration in an infinite linearly elastic cavity near a circular cavity with the propagation of longitudinal harmonic waves was solved. Due to the fact that long-term seismic waves, as a rule, exceed the characteristic dimensions of the cross section designs (for example, diameter D), when solving diffraction problems, it is necessary to consider long-wave effects (

Methods

Results

Conclusion