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

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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 ...

“…Axisymmetric wave motion in a fluid-filled elastic cylinder is described using the complete system of equations of dynamic elasticity and the equation of motion of a perfect fluid [4,16].…”

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

confidence: 99%

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

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Localization of wave motions in a fluid-filled cylinder

Komissarova

2008

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“…The majority of solutions is based on a perfect rigid-plastic model [4, 10, etc.]. As a rule, such solutions are approximate, based on extreme principles of the dynamics of a rigid-plastic body [6], and describe the behavior of homogeneous isotropic plates of constant thickness, with the dependence of the yield stress on the strain rate being neglected [22][23][24][25].For the last decades, slabs reinforced with high-strength bars (fibers) have been used in engineering as effective protective elements. The study into the inelastic dynamic deformation of such structures is in its initial stage [12].…”

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Viscoplastic deformation of reinforced plates with varying thickness under explosive loads

Nemirovskii

Yankovskii

2008

The problem of viscoplastic bending of reinforced plates with varying thickness is formulated. An original method for the integration of this initial-boundary-value problem is developed. The numerical solution is compared with an analytical solution obtained with a rigid-plastic model of an isotropic circular plate. The efficiency of the method is demonstrated by analyzing the inelastic dynamics of reinforced plates with constant and varying thickness. It is shown that the maximum residual deflections of plates can be reduced severalfold by means of rational profiling and reinforcement Keywords: reinforced plate, explosive loading, inelastic dynamics, viscoplastic bending, rational shaping and reinforcementIntroduction. Plates and slabs are the basis of many safety barriers and responsible members in marine, mechanical, and aircraft engineering and building structures. Their damageability under high dynamic loads determines, in many respects, whether they can be in operation afterwards. Therefore, dynamic design of such structural members is one of the major challenges in solid mechanics. The majority of solutions is based on a perfect rigid-plastic model [4, 10, etc.]. As a rule, such solutions are approximate, based on extreme principles of the dynamics of a rigid-plastic body [6], and describe the behavior of homogeneous isotropic plates of constant thickness, with the dependence of the yield stress on the strain rate being neglected [22][23][24][25].For the last decades, slabs reinforced with high-strength bars (fibers) have been used in engineering as effective protective elements. The study into the inelastic dynamic deformation of such structures is in its initial stage [12]. The rationally chosen thickness of a plate is known to influence considerably its resistance (including dynamic) to external loads, and the dependence of the yield stresses of the phases (e.g., steels [3]) of the composition may be considerable, thus affecting the deformability of thin-walled structures under dynamic loading. For example, neglecting this dependence is one of the reasons why the calculated values of residual deflections are 30-80% greater [10] than their experimental values.The objective of the present study is to develop a method to solve an initial-boundary-value problem of dynamic viscoplastic bending of reinforced plates with constant and varying thickness taking into account the viscoplastic hardening of the phases and to analyze the effect of the structure of reinforcement and the profile of plates on their residual deflections under explosive loads.1. Viscoplastic Dynamics of Reinforced Plates. Problem Formulation. Consider a plate with varying thickness H consisting of an isotropic matrix and fine-fibered homogeneous reinforcement of constant cross-section and subjected to transverse dynamic bending. Assume that the reinforcement is regular and quasihomogeneous across the thickness of the plate.To describe the plate, we choose an orthogonal (possibly, curvilinear) coordinate system x 1 , x 2 , z such that the p...

Dynamics of an elastic cylindrical shell with a gas–liquid medium subject to two-frequency vibrational excitation

Lakiza

2008

The paper presents experimental results on nonlinear dynamic processes such as the deformation of the elastic wall of a cylindrical shell filled with a fluid and the formation and clustering of gas bubbles, which interact under two-frequency excitation Keywords: gas-liquid medium, elastic cylindrical shell, bubble cluster, two-frequency excitation Introduction. Many studies [1-3, 10-17, etc.] address the dynamic behavior of a gas-liquid medium in tanks of various shapes and the nonlinear deformation of elastic elements of fluid-filled shells, especially resulting from the interaction with clusters of gas bubbles under single-frequency vibrational excitation. Power plants in real operation conditions and gas-liquid media in tanks of various shapes during various processes are subjected to complex vibrational loads. In this connection, the dynamic behavior of a gas-liquid medium in cylindrical, spherical, and ellipsoidal rigid shells under two-frequency excitation was studied in [1,4,5].The present paper discusses experimental results on the nonlinear dynamic deformation of the elastic wall of a cylindrical shell, the formation and clustering of gas bubbles, and the motion of the gas-liquid medium, which interact under two-frequency vibrational excitation. We will establish and analyze the resonant relations between the two excitation frequencies and the natural frequencies of the shell-fluid system that lead to the most intensive deformation of the tank wall and the free liquid surface and to the most intensive motion of the gas-liquid medium, especially when a nonlinear vibrating liquid-gas system forms.1. Test Models, Equipment, and Procedure. The subject of the experiment is organic-glass shells of height Í sh = 500 and 600 mm, inside diameter D sh = 100 mm, and wall thickness d sh = 1 and 2 mm. A VÉDS-100 electrodynamic shaker was used to excite vibrations of the shells. To produce two-frequency vibrational excitation, we used a generator built in the frame of the shaker and an external Robotron generator. One of them was used for one-frequency excitation. The vibroaccelerations of the shaker table and shell walls were measured with D-14 and IS-318 transducers operating with the measuring unit of the shaker and D-3 and AD-19 (microsensor having a mass of about 1 g) transducers operating with a VShV-3 device. The signals from the transducers were analyzed by a Brüel & Kjaer type 2031 frequency analyzer.It was shown in [1, 3, 16] that a cluster of gas bubbles present in an elastic shell subject to single-frequency vibrational excitation greatly intensifies the nonlinear deformation of the shell wall and the chaotic motion of the gas-liquid medium compared with the case of absence of such a cluster. Moreover, the bubbling in the vibrating fluid due to the resonances of the hydrosystem, which is accompanied by the formation of a nonlinear vibrating liquid-gas system [1,3,6] (with the bubble cluster as an elastic element and the liquid column over it as an inertial element), changes the behavior of the shell [1,7]...