Features of the dynamic deformation of a hollow cylinder

Гринченко, В. Т.; Komissarova, G. L.

doi:10.1007/bf00888535

Cited by 3 publications

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“…The effect of the relative inner radius r 1 of an empty steel cylinder on the cutoff frequencies of radial and longitudinal-shear waves was analyzed in [5]. It was shown that as r 1 increases (the thickness of the cylinder decreases), the cutoff frequency of the longitudinal-shear mode (second normal wave) increases and the cutoff frequency of the radial mode (third normal wave) decreases.…”

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

confidence: 99%

“…The dispersion characteristics of waves in a hollow cylinder depend on not only Poisson's ratio but also the radius of curvature and wall thickness of the cylinder. The thickness most strongly affects the behavior of the normal lowest wave and the distribution of cutoff frequencies of the second and third normal waves [5]. In thin-walled cylinders, minor changes in the frequency cause considerable changes in the length of the normal lowest wave [6,13].…”

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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 Spectrum Of A Fluid-filled Cylindermentioning

confidence: 99%

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confidence: 99%

Localization of wave motions in a fluid-filled cylinder

Komissarova

2008

Int Appl Mech

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Propagation of Normal Axisymmetric Waves in Compliant Elastic Cylinders Filled with and Immersed in a Fluid

Komissarova

2004

International Applied Mechanics

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Free and forced vibrations of hollow elastic cylinders of finite length

Ebenezer

Ravichandran

Padmanabhan

2015

The Journal of the Acoustical Society of America

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An analytical model of axisymmetric vibrations of hollow elastic circular cylinders with arbitrary boundary conditions is presented. Free vibrations of cylinders with free or fixed boundaries and forced vibrations of cylinders with specified non-uniform displacement or stress on the boundaries are considered. Three series solutions are used and each term in each series is an exact solution to the exact governing equations of motion. The terms in the expressions for components of displacement and stress are products of Bessel and sinusoidal functions and are orthogonal to each other. Complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two, respectively. It is therefore possible to satisfy arbitrary boundary conditions. It is shown that just two terms in each series are sufficient to determine several resonance frequencies of cylinders with certain specified boundary conditions. The error is less than 1%. Numerical results are also presented for forced vibration of hollow steel cylinders of length 10 mm and outer diameter 10 mm with specified normal displacement or stress. Excellent agreement with finite element results is obtained at all frequencies up to 1 MHz. Convergence of the series is also discussed.

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Features of the dynamic deformation of a hollow cylinder

Cited by 3 publications

References 1 publication

Localization of wave motions in a fluid-filled cylinder

Localization of wave motions in a fluid-filled cylinder

Propagation of Normal Axisymmetric Waves in Compliant Elastic Cylinders Filled with and Immersed in a Fluid

Free and forced vibrations of hollow elastic cylinders of finite length

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