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

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.

Vibrations of a cylindrical piezoshell filled with a fluid

Stationary oscillations of a piezoceramic cylindrical shell with thickness polarization under the action of a time-harmonic mechanical load in the form of an external pressure are considered. The shell has a finite length and is closed at the ends with rigid plates. The inner volume of the shell is filled with a non-viscous compressible liquid. A continuous thin electrode coating is applied to the cylindrical surfaces of the shell. Surface electrodes are considered open. The equations of axisymmetric oscillations and the corresponding boundary conditions at the ends are written in the problem statement for the shell. A problem is formulated also for determining the motion in the form of small oscillations of a liquid inside the shell, as well as the boundary conditions for the equality of velocities of liquid particles and the shell on their contact surfaces. An analytic expression is given for determining the distribution of the thickness component of the electric field strength, which arises due to the deformation of the shell element, depending on the frequency of oscillations of the external mechanical load. The results of numerical calculations are shown.

Microbubble dynamics in a viscous compressible liquid near a rigid boundary

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.

Acoustic energy radiated by nonlinear spherical oscillations of strongly driven bubbles

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.