Solution of a problem concerning propagation of elastic waves in a fluid-containing cylinder

Komissarova, G. L.

doi:10.1007/bf00891788

Cited by 2 publications

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“…The dispersion equation is a quintic determinant (see [4] for explicit expressions of its elements) equated to zero. The dispersion equation relates the dimensionless frequency g 2 and the wave number V for preset values of Poisson's ratio n, the ratios of velocitiesV C S / 0 and densities r r Many data on the properties of cylindrical elastic-liquid waveguides are presented in [4,6,12,13] for rigid materials and in [7] for compliant materials. There, primary attention was focused on the elastic-liquid interaction in a waveguide and its effect on the dispersion, kinematic, and energy characteristics of normal waves.…”

Section: Analysis Of the Dispersion Equation Of A Fluid-filled Cylindermentioning

confidence: 99%

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Localization of wave motions in a fluid-filled cylinder

Komissarova

2008

Int Appl Mech

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The properties of harmonic surface waves in a fluid-filled cylinder made of a compliant material are studied. The wave motions are described by a complete system of dynamic equations of elasticity and the equation of motion of a perfect compressible fluid. An asymptotic analysis of the dispersion equation for large wave numbers and a qualitative analysis of the dispersion spectrum show that there are two surface waves in this waveguide system. The first normal wave forms a Stoneley wave on the inside surface with increase in the wave number. The second normal wave forms a Rayleigh wave on the outside surface. The phase velocities of all the other waves tend to the velocity of the shear wave in the cylinder material. The dispersion, kinematic, and energy characteristics of surface waves are analyzed. It is established how the wave localization processes differ in hard and compliant materials of the cylinder Keywords: fluid-filled elastic cylinder, dispersion equation, asymptotic analysis, wave number, first and second normal waves, Stoneley and Rayleigh waves, hard and compliant materialsIntroduction. Since Rezal', Gromeko, Kortevoi, and Zhukovski who studied wave motions in fluid-filled pipes, both hard and soft (compliant) materials of the pipe have been considered [11]. They derived approximate expressions for the phase velocity of the lowest normal wave. Study of the properties of normal waves in fluid-filled cylinders is stimulated by a number of applied problems. Of interest are normal waves of low and high orders.An analysis of accumulated data on the properties of normal waves in compound waveguides such as an elastic body with a fluid shows that it is expedient to systematize them by estimating the ratio between the speed of sound in the fluid and the velocity of shear waves in the material of the cylinder [16,17]. If the latter exceeds the former ( ) V C S > 0 , the phase velocities of all normal waves in the compound waveguide, except for the lowest one, tend from above to the speed of sound in the fluid [16]. We will call the associated material of the cylinder hard. If the velocity of shear waves is lower than the speed of sound in the fluid ( ) V C S < 0 , the material of the cylinder will be called soft or compliant. The density of the compliant material is slightly greater than or equal to the density of the fluid. The density of the hard material is much greater than the density of the fluid.Rayleigh and Stoneley were the first to study surface waves in an elastic body [18,21]. The classical Rayleigh wave exists near the free flat surface of an elastic half-space. The Stoneley wave can exist at the flat interface between two elastic media. This wave exists only at certain ratios between the stiffness characteristics of the contacting media [3]; and there are a limited number of pairs of materials with such characteristics. Stoneley waves always exist at the interface between liquid and elastic media [10,20].The Rayleigh and Stoneley waves are monochromatic and nondispersive (the phase velocity is ...

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Section: Analysis Of the Dispersion Equation Of A Fluid-filled Cylindermentioning

confidence: 99%

“…However, the elastic-liquid interaction may strongly affect the localization of wave motions in compound waveguides. The elastic-liquid interaction in a fluid-filled cylinder was analyzed in [4,6,7,12,13] in the axisymmetric case.…”

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confidence: 99%

Localization of wave motions in a fluid-filled cylinder

Komissarova

2008

Int Appl Mech

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“…Quantitative data on and qualitative analysis of the dispersion properties of normal waves in a cylinder with fluid can be found in [4,5,10,11] for hard materials and a wide range of frequencies and wave numbers. The influence of the wall thickness of the cylinder on the dispersion properties of normal waves in a range of relative inner radius r 1 from 0.3 to 0.99 (h/R = 1 -r 1 , h is the wall thickness) was analyzed in [5,11].…”

Section: Analysis Of the Dispersion Spectrum Of A Fluid-filled Cylindermentioning

confidence: 99%

Features of how surface waves form in a cylinder made of a hard material and filled with a fluid

Komissarova

2007

Int Appl Mech

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The properties of harmonic surface waves in an elastic cylinder made of a rigid material and filled with a fluid are studied. The problem is solved using the dynamic equations of elasticity and the equations of motion of a perfect compressible fluid. It is shown that two surface (Stoneley and Rayleigh) waves exist in this waveguide system. The first normal wave generates a Stoneley wave on the inner surface of the cylinder. If the material is rigid, no normal wave exists to transform into a Rayleigh wave. The Rayleigh wave on the outer surface forms on certain sections of different dispersion curves. The kinematic and energy characteristics of surface waves are analyzed. As the wave number increases, the phase velocities of all normal waves, except the first one, tend to the sonic velocity in the fluid from above

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Solution of a problem concerning propagation of elastic waves in a fluid-containing cylinder

Cited by 2 publications

References 2 publications

Localization of wave motions in a fluid-filled cylinder

Localization of wave motions in a fluid-filled cylinder

Features of how surface waves form in a cylinder made of a hard material and filled with a fluid

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