The acoustic field in a rigid cylindrical vessel excited by a sphere oscillating by a definite law

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

doi:10.1007/bf02681985

Cited by 17 publications

(16 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was shown in [21] that the determinant of a system of the form (3.16) is of normal type. Thus, this system of equations has a unique bounded solution [5], which can be found by truncating the infinite system of equations.…”

Section: Satisfying Boundary Conditionsmentioning

confidence: 99%

“…It was assumed that the spherical source is on the cavity axis (axial symmetry). The oscillation of a sphere in a rigid cylindrical cavity filled with a compressible fluid was studied in [21] in the axisymmetric case. The interaction of a rigid cylindrical cavity with a finite number of spherical inclusions in a compressible fluid was studied in [7].…”

mentioning

confidence: 99%

“…The analysis of the phenomena in this system conducted below is mainly based on the studies [6,7,16,20,21].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Resonant phenomena in a cylindrical shell containing a spherical inclusion and immersed in an elastic medium

Kubenko

Dzyuba

2006

Int Appl Mech

Self Cite

View full text Add to dashboard Cite

A method is proposed to investigate the behavior of an axisymmetric system consisting of an infinite thin elastic cylindrical shell immersed in an infinite elastic medium, filled with a perfect compressible fluid, and containing an oscillating spherical inclusion. The system is subjected to periodic excitation. The task is to detect so-called resonant phenomena, to establish conditions that cause them, and to examine the possibilities of using the characteristic parameters of such a hydroelastic system to influence these conditions. The method allows transforming the general solutions of mathematical physics equations from one coordinate system to another to obtain exact analytic solutions (in the form of Fourier series) to interaction problems for systems of rigid and elastic bodies Introduction. The diffraction of sound by an elastic shell as well as the forced vibrations of shells with a fluid were studied extensively (see [8, 9, 14, 17-19, etc.]). For example, a solution describing the scattering of sound by both infinite and axially finite hollow cylindrical shells was found in [8,9] for arbitrary angles of incidence. The acoustic field inside a thin elastic shell filled with some medium was analyzed in [13]; and a solution for a shell of arbitrary thickness was found in [15]. Results from studies on diffraction of waves in an elastic medium are reported in [2,3]. In the cited and other publications, diffraction problems were solved for either single bodies or systems of similar surfaces: families of parallel cylinders or spherical (spheroidal) bodies.The present paper deals with an axisymmetric system consisting of an infinite thin elastic cylindrical shell containing an oscillating spherical inclusion, immersed in an infinite elastic medium, and filled with a compressible fluid. The analysis of the phenomena in this system conducted below is mainly based on the studies [6,7,16,20,21].A potential describing the pulsation of a sphere in a compressible (acoustic approximation) fluid filling a circular cylindrical cavity was constructed in [6]. It was assumed that the spherical source is on the cavity axis (axial symmetry). The oscillation of a sphere in a rigid cylindrical cavity filled with a compressible fluid was studied in [21] in the axisymmetric case. The interaction of a rigid cylindrical cavity with a finite number of spherical inclusions in a compressible fluid was studied in [7]. A potential describing the prescribed motion of a spherical body in a compressible fluid filling a thin elastic cylindrical shell was derived in [20], wherein solutions of specific problems are presented.The analysis of the dynamic behavior of the hydroelastic systems in question is reduced here to the simultaneous solution of equations modeling the motion of a perfect compressible fluid, a thin elastic shell, and an elastic medium. Such models are the acoustic approximation, the theory of thin elastic shells based on the Kirchhoff-Love hypotheses, and the Lamé equations. The solution technique is based on the possibility o...

show abstract

Section: Satisfying Boundary Conditionsmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Resonant phenomena in a cylindrical shell containing a spherical inclusion and immersed in an elastic medium

Kubenko

Dzyuba

2006

Int Appl Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…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.…”

mentioning

confidence: 92%

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

2006

Self Cite

View full text Add to dashboard Cite

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...

show abstract

“…In contrast to the numerous research works which treat a point source in an acoustic borehole, there are very few theoretical analyses relating a finite size (spherical or cylindrical) source in a cylindrical cavity (waveguide). In a series of papers, Kubenko and coworkers employed the axisymmetric cylindrical to spherical wave transformations to study the acoustic field in a rigid cylindrical vessel excited by an internal finite spherical oscillator [6], the dynamic interaction between an oscillating sphere and an encapsulating thin elastic cylindrical shell filled with (immersed in) a compressible liquid [7,8], the dynamic interaction of a semi-infinite elastic cylindrical shell with liquid containing a vibrating spherical segment [9], and the dynamic interaction of an oscillating sphere and an encapsulating fluid-filled elastic cylindrical shell embedded in an elastic medium [10]. Considering a uniform circular cylinder of unlimited length suspended in a fluid-filled cylindrical cavity as an idealized model of an acoustic logging tool [11], Poterasu [12] investigated dynamic coupling effects for a pulsating source in a fluid-filled cavity embedded within an (ideal) elastic infinite media by the boundary element method.…”

Section: Introductionmentioning

confidence: 99%

Dynamic interaction of an eccentric multipole cylindrical radiator suspended in a fluid-filled borehole within a poroelastic formation

Hasheminejad

Miri

2007

Acta Mech Sin

View full text Add to dashboard Cite

Acoustic radiation and the dynamic field induced by a cylindrical source of infinite extent, undergoing angularly periodic and axially-dependent harmonic surface vibrations, while eccentrically suspended in a fluid-filled cylindrical cavity embedded within a fluid-saturated porous elastic formation, are analyzed in an exact manner. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole within a permeable surrounding formation, is of practical importance with a multitude of possible applications in seismo-acoustics. The formulation utilizes the novel features of Biot dynamic theory of poroelasticity along with the translational addition theorem for cylindrical wave functions to obtain a closedform series solution. The basic dynamic field quantities such as the resistive and the reactive components of the modal acoustic radiation impedance load on the source in addition to the radial and transverse stresses induced in the surrounding formation by an eccentric pulsating/oscillating cylinder in a water-filled borehole within a water-saturated Ridgefield sandstone medium are evaluated and discussed. Special attention is paid to the effects of source eccentricity, excitation frequency, and mode of surface oscillations on the modal impedance values and the dynamic stresses. Limiting cases are considered and good agreements with available solutions are obtained.

show abstract

The acoustic field in a rigid cylindrical vessel excited by a sphere oscillating by a definite law

Cited by 17 publications

References 3 publications

Resonant phenomena in a cylindrical shell containing a spherical inclusion and immersed in an elastic medium

Resonant phenomena in a cylindrical shell containing a spherical inclusion and immersed in an elastic medium

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

Dynamic interaction of an eccentric multipole cylindrical radiator suspended in a fluid-filled borehole within a poroelastic formation

Contact Info

Product

Resources

About