Wave propagation in a cylindrical shell containing a viscous compressible liquid

1980 ◽  
Vol 16 (10) ◽  
pp. 842-850
Author(s):  
A. N. Guz'
Keyword(s):  
Cylindrical Shell ◽  
Wave Propagation ◽  
Compressible Liquid ◽  
Viscous Compressible Liquid

Wave Propagation in Viscous, Compressible Liquids Confined in Elastic Tubes

1972 ◽  
Vol 94 (4) ◽  
pp. 811-816 ◽  
Author(s):  
R. P. DeArmond ◽  
W. T. Rouleau
Keyword(s):  
Wave Propagation ◽  
Acoustic Waves ◽  
Propagation Distance ◽  
Periodic Wave ◽  
Elastic Tube ◽  
Compressible Liquid ◽  
The Other ◽  
Elastic Tubes ◽  
Viscous Compressible Liquid ◽  
Speed Of Propagation

The problem of steady-state, small amplitude, periodic wave propagation in a viscous, compressible liquid contained in an infinitely long, elastic tube is solved for the complex propagation constants of the two lowest modes of motion. One mode has a speed of propagation and decay constant characteristic of acoustic waves propagating in a liquid; the other mode corresponds to acoustic waves propagating in an elastic tube. The behavior of these two modes is investigated as a function of frequency, viscosity, and tube rigidity. A third mode of motion corresponding to edge loads on the tube is also investigated. This mode, unlike the other two modes, is characterized by a cut-off frequency above which the propagation distance is infinite and below which it is finite.

scholarly journals Longitudinal vibrations of a cylindrical shell filled with a viscous compressible liquid

2021 ◽  
Vol 264 ◽  
pp. 02017
Author(s):  
Khayrulla Khudoynazarov ◽  
Burxon Yalgashev
Keyword(s):  
Cylindrical Shell ◽  
Compressible Fluid ◽  
Elastic Shell ◽  
Compressible Liquid ◽  
Viscous Compressible Fluid ◽  
Longitudinal Displacement ◽  
Longitudinal Vibrations ◽  
Radial Displacements ◽  
Viscous Compressible Liquid ◽  
External Loads

This article investigates the longitudinal vibrations of a semi-infinite circular cylindrical elastic shell filled with a viscous compressible fluid. It is believed that the vibrations are excited by a suddenly switched on longitudinal displacement at the end. To solve the problem, the refined equations of longitudinal vibrations of a circular cylindrical elastic shell interacting with an internal viscous compressible fluid, previously proposed by the authors, were taken as the main resolving equations. In this case, the lateral surfaces of the shell are considered free from external loads; in addition, considering purely longitudinal vibrations, it can be assumed that the radial displacements of the points of the shell are equal to zero.

Acoustic energy radiated by nonlinear spherical oscillations of strongly driven bubbles

2010 ◽  
Vol 466 (2118) ◽  
pp. 1829-1847 ◽  
Author(s):  
Joachim Holzfuss
Keyword(s):  
Wave Model ◽  
High Amplitude ◽  
Compressible Liquid ◽  
Acoustic Energy ◽  
Compressible Medium ◽  
Relevant Parameter ◽  
Wafer Cleaning ◽  
Viscous Compressible Liquid ◽  
Shock Wave Model ◽  
Polytropic Exponent

Based on the theory of F. Gilmore ( Gilmore 1952 The growth or collapse of a spherical bubble in a viscous compressible liquid ) for radial oscillations of a bubble in a compressible medium, the sound emission of bubbles in water driven by high-amplitude ultrasound is calculated. The model is augmented to include expressions for a variable polytropic exponent, hardcore and water vapour. Radiated acoustic energies are calculated within a quasi-acoustic approximation and also a shock wave model. Isoenergy lines are shown for driving frequencies of 23.5 kHz and 1 MHz. Together with calculations of stability against surface wave oscillations leading to fragmentation, the physically relevant parameter space for the bubble radii is found. Its upper limit is around 6 μm for the lower frequency driving and 1–3 μm for the higher. The radiated acoustic energy of a single bubble driven in the kilohertz range is calculated to be of the order of 100 nJ per driving period; a bubble driven in the megahertz range reaches two orders of magnitude less. The results for the first have applications in sonoluminescence research. Megahertz frequencies are widely used in wafer cleaning, where radiated sound may be implicated as responsible for the damage of nanometre-sized structures.

scholarly journals Microbubble dynamics in a viscous compressible liquid near a rigid boundary

2019 ◽  
Vol 84 (4) ◽  
pp. 696-711 ◽  
Author(s):  
Qianxi Wang ◽  
WenKe Liu ◽  
David M Leppinen ◽  
A D Walmsley
Keyword(s):  
Potential Flow ◽  
Stokes Equations ◽  
Bubble Surface ◽  
Compressible Liquid ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Viscous Effects ◽  
Rigid Boundary ◽  
Viscous Potential Flow ◽  
Viscous Compressible Liquid

Abstract This paper is concerned with microbubble dynamics in a viscous compressible liquid near a rigid boundary. The compressible effects are modelled using the weakly compressible theory of Wang & Blake (2010, Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave. J. Fluid Mech., 730, 245–272), since the Mach number associated is small. The viscous effects are approximated using the viscous potential flow theory of Joseph & Wang (2004, The dissipation approximation and viscous potential flow. J. Fluid Mech., 505, 365–377), because the flow field is characterized as being an irrotational flow in the bulk volume but with a thin viscous boundary layer at the bubble surface. Consequently, the phenomenon is modelled using the boundary integral method, in which the compressible and viscous effects are incorporated into the model through including corresponding additional terms in the far field condition and the dynamic boundary condition at the bubble surface, respectively. The numerical results are shown in good agreement with the Keller–Miksis equation, experiments and computations based on the Navier–Stokes equations. The bubble oscillation, topological transform, jet development and penetration through the bubble and the energy of the bubble system are simulated and analysed in terms of the compressible and viscous effects.

scholarly journals Free Vibration Characteristics of Cylindrical Shells Using a Wave Propagation Method

2001 ◽  
Vol 8 (2) ◽  
pp. 71-84 ◽  
Author(s):  
A. Ghoshal ◽  
S. Parthan ◽  
D. Hughes ◽  
M.J. Schulz
Keyword(s):  
Cylindrical Shell ◽  
Wave Propagation ◽  
Free Vibration ◽  
Periodic Structure ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Structural Element ◽  
Lower Bounding ◽  
Nodal Points ◽  
Wave Propagation Method

In the present paper, concept of a periodic structure is used to study the characteristics of the natural frequencies of a complete unstiffened cylindrical shell. A segment of the shell between two consecutive nodal points is chosen to be a periodic structural element. The present effort is to modify Mead and Bardell's approach to study the free vibration characteristics of unstiffened cylindrical shell. The Love-Timoshenko formulation for the strain energy is used in conjunction with Hamilton's principle to compute the natural propagation constants for two shell geometries and different circumferential nodal patterns employing Floquet's principle. The natural frequencies were obtained using Sengupta's method and were compared with those obtained from classical Arnold-Warburton's method. The results from the wave propagation method were found to compare identically with the classical methods, since both the methods lead to the exact solution of the same problem. Thus consideration of the shell segment between two consecutive nodal points as a periodic structure is validated. The variations of the phase constants at the lower bounding frequency for the first propagation band for different nodal patterns have been computed. The method is highly computationally efficient.

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