Propagation of axially symmetric elastic vibrations along a waveguide in an elastic medium

S. L. Davydov; G. G. Zaretskii-Feoktistov; V. V. Sudakov

doi:10.1007/bf00856428

Axially Symmetric Stress Distributions in Elastic Solids Containing Ring-Shaped Cracks Under Torsion

Journal of Applied Mechanics ◽

10.1115/1.3423320 ◽

1974 ◽

Vol 41 (2) ◽

pp. 516-517 ◽

Cited By ~ 4

Author(s):

R. P. Kanwal ◽

M. L. Pasha

Keyword(s):

Elastic Medium ◽

Crack Problem ◽

Outer Radius ◽

Stress Distributions ◽

Axially Symmetric ◽

Elastic Solids ◽

First Case

We present the axially symmetric stress distributions in elastic solids containing ring-shaped cracks when the solids are kept under torsion. Two cases are analyzed. In the first case we discuss the crack problem in an infinite elastic medium when the ratio of the inner to the outer radius is small. In the second case this ratio is almost equal to unity.

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Axially Symmetric Stress Distributions in Elastic Solids Containing Penny-Shaped Cracks Under Torsion

Journal of Applied Mechanics ◽

10.1115/1.3423735 ◽

1975 ◽

Vol 42 (4) ◽

pp. 896-897 ◽

Cited By ~ 9

Author(s):

M. L. Pasha

Keyword(s):

Stress Intensity ◽

Integral Representation ◽

Elastic Medium ◽

Stress Intensity Factors ◽

Representation Formula ◽

Stress Distributions ◽

Axially Symmetric ◽

Intensity Factors ◽

Elastic Solids ◽

Integral Representation Formula

We present the axially symmetric stress distributions in elastic solids containing a pair of axially symmetric penny shaped cracks when the infinite elastic medium is kept under torsion. We derive the integral representation formula for the torsion function and the expressions for the stress-intensity factors.

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Analysis of the spectrum of elastic vibrations of a rod in a nonuniform elastic medium

Doklady Physics ◽

10.1134/s1028335810070104 ◽

2010 ◽

Vol 55 (7) ◽

pp. 353-356

Author(s):

L. D. Akulenko ◽

S. V. Nesterov

Keyword(s):

Elastic Medium ◽

Elastic Vibrations

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Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells

Symmetry ◽

10.3390/sym13112227 ◽

2021 ◽

Vol 13 (11) ◽

pp. 2227

Author(s):

Andrey Bochkarev ◽

Aleksandr Zemlyanukhin ◽

Vladimir Erofeev ◽

Aleksandr Ratushny

Keyword(s):

Elastic Medium ◽

Gordon Equation ◽

Modulation Instability ◽

Solvable Models ◽

Axially Symmetric ◽

Wave Dynamics ◽

Periodic Traveling Waves ◽

Bending Waves ◽

Klein Gordon ◽

Nonlinear Elastic

The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obtained that have no physically realizable solitary wave solutions. The possibility for the real existence of exact solutions, in the form of traveling periodic waves of the nonlinear inhomogeneous Klein–Gordon equation, was established. Two cases were identified, which enabled the development of the modulation instability of periodic traveling waves: (1) a shell preliminarily compressed along a generatrix, surrounded by an elastic medium with hard nonlinearity, and (2) a preliminarily stretched shell interacting with an elastic medium with soft nonlinearity.

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Transient stresses in an elastic half space resulting from the frictionless indentation of a rigid axially symmetric conical die

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100049008 ◽

1974 ◽

Vol 76 (1) ◽

pp. 369-379 ◽

Cited By ~ 5

Author(s):

A. R. Robinson ◽

J. C. Thompson

Keyword(s):

Elastic Medium ◽

Half Space ◽

Elastic Half Space ◽

Theory Of Elasticity ◽

Axially Symmetric ◽

Transient Stress ◽

Conical Die ◽

Constant Rate ◽

Title Problem ◽

Stress States

AbstractA solution which is exact within the framework of the classical theory of elasticity is obtained for the title problem assuming that the half space is homogeneous and isotropic, and that the die indents at a constant rate. If the shape of the die and the elastic medium are specified, the rate of indentation uniquely determines the outward speed of the edge of the expanding contact zone. The magnitude of this speed, relative to the speeds of the dilatational, rotational and Rayleigh waves in the elastic medium, determines which of four possible characteristic transient stress states will occur. Each of the four ranges of contact speed is solved by the method of rotational superposition of self-similar potentials which is briefly described in the Appendix.

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The Lagrangian Function and Separation of Variables for Elastic Vibrations in Axially Symmetric Layered media

Computational Seismology and Geodynamics - Selected Papers from Volumes 26 and 27 of Vychislitel'naya Seysmologiya ◽

10.1029/cs003p0183 ◽

2013 ◽

pp. 183-192 ◽

Cited By ~ 3

Author(s):

A. N. Kuznetsov

Keyword(s):

Separation Of Variables ◽

Layered Media ◽

Lagrangian Function ◽

Axially Symmetric ◽

Elastic Vibrations

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Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

International Astronomical Union Colloquium ◽

10.1017/s0252921100064861 ◽

2000 ◽

Vol 179 ◽

pp. 379-380

Author(s):

Gaetano Belvedere ◽

Kirill Kuzanyan ◽

Dmitry Sokoloff

Keyword(s):

Magnetic Field ◽

Asymptotic Solution ◽

Internal Rotation ◽

Convection Zone ◽

General Idea ◽

Dynamo Model ◽

Axially Symmetric ◽

Dynamo Action ◽

Regeneration Rate ◽

Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

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