Axisymmetric Wave Propagation in the Initially Twisted Circular Compound Cylinders

2009 ◽  
Author(s):  
Surkay Akbarov ◽  
Mugan Guliev
Keyword(s):  
Wave Propagation ◽  
Solution Method ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Homogeneous Body ◽  
Body Model ◽  
Axisymmetric Wave ◽  
Piecewise Homogeneous Body ◽  
Linearized Theory ◽  
Circular Compound

Within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic wave propagation in an initially stressed body, the problem of the axisymmetric wave propagation in an initially twisted circular compound cylinders is studied. The mathematical formulation of the problem is presented and the corresponding solution method is proposed and developed, following which the numerical results are presented and discussed. In particular, it is established that as a result of the initial twisting of the circular compound cylinders, new axisymmetric wave modes arise.

On Some Particularities of the Axisymmetric Wave Propagation in the Initially Twisted Circular Compound Cylinders

2010 ◽  
Author(s):  
Surkay Akbarov ◽  
Mugan Guliev ◽  
Tamer Kepceler
Keyword(s):  
Wave Propagation ◽  
Solution Method ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Body Model ◽  
Axisymmetric Wave ◽  
Piecewise Homogeneous Body ◽  
Linearized Theory ◽  
New Type ◽  
Circular Compound

This paper investigates some particularities related with the influence of the magnitude of the initial twisting of the axisymmetric wave propagation in the initially twisted circular bi-material compounded cylinder. The investigation is carried out within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic wave propagation in an initially stressed body. The mathematical formulation of the problem is presented and the corresponding solution method is proposed and developed. The numerical results are further presented and discussed. In particular, the mechanism of the arising of the new type modes caused by the initial twisting of the circular compounded cylinders is established.

Statics of Laminated and Fibrous Composites With Curved Structures

1992 ◽  
Vol 45 (2) ◽  
pp. 17-34 ◽  
Author(s):  
S. D. Akbarov ◽  
A. N. Guz’
Keyword(s):  
Composite Material ◽  
Solid Body ◽  
Three Dimensional ◽  
Local Distribution ◽  
Homogeneous Body ◽  
Deformable Solid ◽  
Body Model ◽  
Curved Structures ◽  
Piecewise Homogeneous Body ◽  
Deformable Solid Body

A broad and detailed review is presented on problems of statics of mechanics of laminated and fibrous composite materials with curved structures. Studies are discussed which were carried out based on the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics. The classification was made according to the type of composite (laminated, fibrous), the form of bending in the structure of composites considered, the materials properties (isotropic, anisotropic), the properties of binder and filler, and their models (elastic, viscoelastic). The formulation of the problem is presented for laminated and fibrous composites with bent, curved structures. Two types of bending are distinguished according to the forms of reinforcing elements bending: (1) periodic; (2) local. For every type of bending, solution methods of corresponding problems are presented. Moreover, according to the form of the location of neighboring curved, bent layers, with respect to each other, two types of bending are distinguished—the monophasic and the antiphasic. Detailed presentation is given of some very significant specific results, illustrating the influence of reinforcing element bending on local distribution of stresses in every component of the composite material. Tables and graphs are presented from publications on this subject. Some applications are presented of results based on the piecewise-homogeneous body model in composite mechanics. In conclusion, some areas of future research are proposed. The situations presented prove the theoretical and practical importance of investigations discussed in the review. In the analysis of strength problems, in many cases information is needed on the local distribution of the stress-deformed state in every component of the composite material with bent, curved structures. Information of this type could be obtained only within the framework of the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics.

scholarly journals Influence of shear effects on the characteristics of axisymmetric wave propagation in a buried fluid-filled pipe

2020 ◽  
Author(s):  
Ping Lu ◽  
Xiaozhen Sheng ◽  
Yan Gao ◽  
Ruichen Wang
Keyword(s):  
Wave Propagation ◽  
Pipe Wall ◽  
Surrounding Medium ◽  
Three Dimensional ◽  
Engineering Application ◽  
Leak Detection ◽  
Calculation Model ◽  
Theoretical Research ◽  
Axisymmetric Wave ◽  
Shear Effects

Abstract The acoustic propagation characteristics of axisymmetric waves have been widely used in leak detection of fluid-filled pipes. The related acoustic methods and equipment are gradually coming to the market, but their theoretical research obviously lags behind the field practice, which seriously restricts the breakthrough and innovation of this technology. Based on the fully three-dimensional effect of the surrounding medium, a coupled motion equation of axisymmetric wave of buried liquid-filled pipes is derived in detail, a contact coefficient is used to express the coupling strength between surrounding medium and pipe, then, a general equation of motion was derived which contain the pipe soil lubrication contact, pipe soil compact contact and pipe in water and air. Finally, the corresponding numerical calculation model is established and solved used numerical method. The shear effects of the surrounding medium and the shear effects at the interface between surrounding medium and pipe are discussed in detail. The output indicates that the surrounding medium is to add mass to the pipe wall, but the shear effect is to add stiffness. With the consideration of the contact strength between the pipe and the medium, the additional mass and the pipe wall will resonate at a specific frequency, resulting in a significant increase in the radiation wave to the surrounding medium. The research contents have great guiding effect on the theory of acoustic wave propagation and the engineering application of leak detection technology in the buried pipe.

scholarly journals Influence of shear effects on the characteristics of axisymmetric wave propagation in a buried fluid-filled pipe

2020 ◽  
Author(s):  
Ping Lu ◽  
Xiaozhen Sheng ◽  
Yan Gao ◽  
Ruichen Wang
Keyword(s):  
Wave Propagation ◽  
Pipe Wall ◽  
Surrounding Medium ◽  
Three Dimensional ◽  
Engineering Application ◽  
Leak Detection ◽  
Calculation Model ◽  
Theoretical Research ◽  
Axisymmetric Wave ◽  
Shear Effects

Abstract The acoustic propagation characteristics of axisymmetric waves have been widely used in leak detection of liquid-filled pipes. The related acoustic methods and equipment are gradually coming to the market, but their theoretical research obviously lags behind the field practice, which seriously restricts the breakthrough and innovation of this technology. Based on the fully three-dimensional effect of the surrounding medium, a coupled motion equation of axisymmetric wave of buried liquid-filled pipes is derived in detail, a contact coefficient is used to express the coupling strength between surrounding medium and pipe, then, a general equation of motion was derived which contain the pipe soil lubrication contact, pipe soil co mpact contact and pipe in water and air. Finally, the corresponding numerical calculation model is established and solved used numerical method. The shear effects of the surrounding medium and the shear effects at the interface between surrounding medium and pipe are discussed in detail. The output indicates that the surrounding medium is to add mass to the pipe wall, but the shear effect is to add stiffness. With the consideration of the contact strength between the pipe and the medium, the additional mass and the pipe wall will resonate at a specific frequency, resulting in a significant increase in the radiation wave to the surrounding medium. The research contents have great guiding effect on the theory of acoustic wave propagation and the engineering application of leak detection technology in the buried pipe.

On the Axisymmetric Torsional Wave Dispersion and Its Controlling in the Finitely Pre-Stretched Bi-Material Compound Circular Cylinder

2010 ◽  
Author(s):  
Tamer Kepceler ◽  
M. Mert Egilmez
Keyword(s):  
Wave Propagation ◽  
Circular Cylinder ◽  
Elastic Waves ◽  
Propagation Velocity ◽  
Three Dimensional ◽  
Wave Dispersion ◽  
Torsional Wave ◽  
Wave Propagation Velocity ◽  
Body Model ◽  
Initial Strains

This paper investigates the dispersion of the torsional wave propagation in the finitely pre-strained bi-material compounded cylinder. This investigation is made within the framework of the piecewise homogenous body model with the use of the three dimensional linear theory of the elastic waves in initially stressed bodies. The mechanical relations of the materials of the components of the cylinder are described by the harmonic potential. The numerical results on the influence of the initial strains on the wave propagation velocity are presented and discussed. It is established in particularly that the initial stretching of the cylinders causes to increase the torsional wave propagation velocity.

scholarly journals Finite Element Formulation of Forced Vibration Problem of a Prestretched Plate Resting on a Rigid Foundation

2007 ◽  
Vol 2007 ◽  
pp. 1-12
Author(s):  
M. Eröz ◽  
A. Yildiz
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Virtual Work ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Virtual Work Principle ◽  
Loading Case ◽  
Linearized Theory

The three-dimensional linearized theory of elastodynamics mathematical formulation of the forced vibration of a prestretched plate resting on a rigid half-plane is given. The variational formulation of corresponding boundary-value problem is constructed. The first variational of the functional in the variational statement is equated to zero. In the framework of the virtual work principle, it is proved that appropriate equations and boundary conditions are derived. Using these conditions, finite element formulation of the prestretched plate is done. The numerical results obtained coincide with the ones given by Ufly and in 1963 for the static loading case.

Torsional Wave Dispersion in a Pre-Strained Hollow Sandwich Cylinder With Soft Core

2011 ◽  
Author(s):  
S. D. Akbarov ◽  
T. Kepceler ◽  
M. Mert Egilmez
Keyword(s):  
Wave Propagation ◽  
Three Dimensional ◽  
Core Layer ◽  
Wave Dispersion ◽  
Torsional Wave ◽  
Wave Number ◽  
Limit Values ◽  
Hyper Elastic ◽  
Linearized Theory ◽  
Initial Strains

In this work a torsional wave dispersion in a pre-strained three-layered (sandwich) hollow circular cylinder made from hyper-elastic materials is studied. It is assumed that the material of the core layer is soft than the materials of skin layers and the investigations are carried out within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies. The mechanical relations of the materials of the cylinders are described through their harmonic potential. The analytical expression is obtained for the low wave number limit values of the torsional wave propagation velocity. Moreover, numerical results on the influence of the problem parameters, such as initial strains arising as a result of the stretching or compression of the cylinders along the torsional wave propagation direction, thickness of the layers, mechanical constants of the layers’ materials and etc, are presented and discussed.

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