Resonance phenomena in cylindrical shell with a spherical inclusion in the presence of an internal compressible liquid and an external elastic medium

Kubenko, V. D.; Dzyuba, V. V.

doi:10.1016/j.jfluidstructs.2006.02.002

Cited by 9 publications

(7 citation statements)

References 25 publications

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“…By considering the velocity as a harmonic function, u s (t) = D • sin(ωt) can be obtained, where D is the amplitude of the vibration. Additionally, the boundary condition can be written as Equation 17below by submitting Equation (16) to Equation (15). The coefficients of C and ϕ can thus be confirmed:…”

Section: Solution Of the Compressive Fluidmentioning

confidence: 97%

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Vibration-Induced Pressures on a Cylindrical Structure Surface in Compressible Fluid

2019

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This paper unprecedentedly addresses the effect of vibrations of a cylindrical structure on dynamic pressures in a compressible and incompressible fluid situation. To obtain analytical solutions, the density of the fluid is simplified as a constant, but the rates of the density with respect to time and to space are considered as a dynamic and time-dependent function. In addition, the low velocity of the vibration is taken into account so the lower order terms are negligible. According to the assumption that the vibration at the boundary of the structure behaves as a harmonic function, some interesting and new analytical solutions can be established. Both analytical solutions in the cases of the compressible and incompressible fluid are rigorously verified by the calibrated numerical simulations. New findings reveal that, in the case of the incompressible fluid, dynamic pressure at the surface of the cylindrical shell is proportional to the acceleration of the vibration, which acts like an added mass. In the case of the compressible fluid, the pressure at the surface of the cylindrical structure is proportional to the velocity of the vibration, which acts as a damping. In addition, the proportional ratio is derived as ρ c .

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Section: Solution Of the Compressive Fluidmentioning

confidence: 97%

“…Actually, his conclusion only fulfilled the 1-D condition. Kubenko, Dzyuba [16] proposed a new method to investigate the behavior of an elastic shell submerged in an unbounded fluid. In his paper, the fluid was assumed to be an elastic medium, and some analytical solutions written as a Fourier series were proposed.…”

Section: Introductionmentioning

confidence: 99%

Vibration-Induced Pressures on a Cylindrical Structure Surface in Compressible Fluid

2019

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“…The results, obtained by the method outlined in the previous papers (see, e.g., [20]), were compared with those for a similar hydroelastic system with a fluid at rest. Figure 2 shows the distribution of the deflection magnitude over the cylindrical surface (in the interval -3 ≤ z ≤ 3) excited by the spherical inclusion vibrating with dimensionless frequency ω = 2.4 (close to the resonant frequency of the fluid column resting in the same cylindrical shell that contains no spherical inclusions [21]) for the following values of the wall thickness, sphere radius, and flow velocity: h = 0.001 (one-thousandth the radius of the shell) and h = 0.01; r 0 = 0.25 (one-quarter the radius of the shell; Fig. 2a), r 0 = 0.5 (half the radius of the shell; Fig.…”

Section: Satisfying the Boundary Conditionsmentioning

confidence: 99%

Interaction of differently shaped bodies in a potential flow of perfect compressible fluid: Axisymmetric internal problem

2006

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An approach is proposed to investigate an axisymmetric system consisting of an infinite thin elastic cylindrical shell that contains a potential flow of perfect compressible fluid and a periodically vibrating spherical inclusion. The approach emerged as part of a project devoted to developing methods to bring plugged oil wells back into production by the Vibration Theory Department of the S. P. Timoshenko Institute of Mechanics. This mathematical approach allows transforming the general solutions to equations of mathematical physics from one coordinate system to another to obtain an exact analytical solution (in the form of Fourier series) to interaction problems for systems of rigid and elastic bodies Keywords: Kirchhoff-Love hypotheses, wave equation, thin-walled elastic cylindrical shell, perfect compressible fluid, spherical inclusion, potential flowIntroduction. The behavior of structural members interacting with a compressible liquid or gas has recently become of great interest. Among the variety of structure-fluid interaction problems, there are problems that are not restricted to the interaction of various structures (bodies) with the fluid, but are also concerned with the interaction between these structures.The interaction of bodies of similar geometry in one medium or another has been studied most adequately because the fact that components of the general solution are described in the same coordinate system makes it much easier to find this solution. This allows using the summation theorems for special functions to express the general solution in the coordinate systems fixed to the bodies. Techniques of solving such problems are outlined, for example, in [1,10,14,19,23].A completely different situation arises with the general solution for interacting bodies of different geometries in one medium or another that is at rest or moving with a certain velocity. Since the components of the general solution are described in different coordinate systems, the summation theorems for special functions are not sufficient to express the general solution in one coordinate system. For this purpose, use is made of expressions that relate cylindrical and spherical wave functions. The validity of these relations was proved in [11,12]. Issues associated with the interaction of differently shaped bodies in a fluid were addressed, for example, in [13,16,18,20,22].The present paper studies an axisymmetric system consisting of an infinitely long, thin-walled, elastic, cylindrical shell that contains a potential flow of perfect compressible fluid and a vibrating spherical inclusion. Our analysis of the phenomena occurring in this system will be mainly based on the monographs and publications [1, 3, 5, 7, 8, 13, 20, etc.].To analyze the dynamic behavior of the hydroelastic system, we will simultaneously solve equations describing the motion of the fluid and the shell. These equations are taken from the linear theory of potential flows and the theory of thin elastic shells based on the Kirchhoff-Love hypotheses. The solution can...

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“…They considered the effects of the compressibility of the fluid and obtained a theoretical result that could predict the fluid-coupled frequencies well. Kubenko et al [18] conducted a number of studies on a cylindrical shell submerged in an unbounded medium. They also assumed the fluid to be an incompressible fluid.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Pressure Analysis of Hemispherical Shell Vibrating in Unbounded Compressible Fluid

2018

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This paper is the first to highlight the vibrations of a hemispherical shell structure interacting with both compressible and incompressible fluids. To precisely calculate the pressure of the shell vibrating in the air, a novel analytical approach has been established that has existed in very few publications to date. An analytical formulation that calculates pressure was developed by integrating both the ‘small-density method’ and the ‘Bessel function method’. It was considered that the hemispherical shell vibrates as a simple harmonic function, and the fluid is non-viscous. For comparison, the incompressible fluid model has been analyzed. Surprisingly, it is the first to report that the pressure of the shell surface is proportional to the vibration acceleration, and the velocity amplitude decreased at the rate of 1 r 2 when the fluid was incompressible. Otherwise, the surface pressure of the hemispherical shell was proportional to the vibration velocity, and the velocity amplitude decreased with the rate of 1 r when the fluid was compressible. The compressibility of fluid played an important role in the dynamic pressure of the shell structure. Furthermore, the scale factor derived by the theoretical approach was the product of the density and the sound velocity of the fluid ( ρ o c ) exactly. In this study, the analytical solutions were verified by the calibrated numerical simulations, and the analytical formulation were rigorously tested by extensive parametric studies. These new findings can be used to guide the optimal design of the spherical shell structure subjected to wind load, seismic load, etc.

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Resonance phenomena in cylindrical shell with a spherical inclusion in the presence of an internal compressible liquid and an external elastic medium

Cited by 9 publications

References 25 publications

Vibration-Induced Pressures on a Cylindrical Structure Surface in Compressible Fluid

Vibration-Induced Pressures on a Cylindrical Structure Surface in Compressible Fluid

Interaction of differently shaped bodies in a potential flow of perfect compressible fluid: Axisymmetric internal problem

Dynamic Pressure Analysis of Hemispherical Shell Vibrating in Unbounded Compressible Fluid

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