Weak pressure wave in a gas filled elastic tube

The propagation of a small but finite shock disturbance through gas contained within a cylindrical tube is examined theoretically for the case where both the hoop elasticity and radial inertia of the tube are taken into account. Governing equations so derived are found to admit a non-dispersive wave of variable pressure behind the advancing shock front in direct contrast with the situation existing for an initially sharp-fronted infinitesimal disturbance where no steady wave form is possible. Detailed calculations are carried out for the case where the gas filling the tube is air. Results show that increases in either the tube or shock strength are sufficient to make the pressure distribution behind the wave front approach that which would exist in a rigid tube under similar conditions.     

Nonlinear wave processes in media containing cracks partially filled with a viscous liquid

A nonlinear (in the cubic approximation) relaxation equation of state is derived for a rod containing cracks partially filled with an incompressible viscous liquid. The nonlinear effects of the self-action and interaction of low-and high-frequency longitudinal elastic waves propagating in such a rod are studied for the cases of identical and size-varied cracks. Linear and nonlinear acoustic parameters characterizing the self-action and interaction of elastic waves in a cracked rod are determined.     

Acoustic nonlinearity of cracks partially filled with a viscous liquid: A quadratic approximation

A mechanism that accounts for the acoustic nonlinearity of cracks partially filled with a viscous liquid is proposed. The mechanism is related to the nonlinear dependences of the capillary and viscous pressures in liquid on the distance between the crack surfaces and on the rate of change of this distance. The nonlinear equation of state is obtained for this type of cracks, and the parameters of this equation are determined. It is shown that the presence of a viscous liquid can lead to a considerable increase in the acoustic nonlinearity of such cracks, as compared to the cracks filled with an ideal liquid.     

Acoustic waves in cylindrical gap,filled by polymeric liquid

Propagation of acoustic waves in thin-walled elastic tube with coaxial internal rigid rod is investigated in conjugated quasi-one-dimensional formulation. The cylindrical gap between the tube's wall and the central rod is filled by polymeric liquid, described by hereditary model with a discrete spectrum. Dynamics of the tube is treated within Kirchhoff-Love approximation. The dispersion equation accounting for viscoelastic effects in the fluid in coupling with inertia, radial and longitudinal deformations of the tube's wall has been obtained. Its analysis has showed strong influence of the liquid's rheological properties and geometrical parameters of the system on pressure signals dispersion and attenuation. The results can be used for rheological characterization of polymeric liquids by acoustic means.     

Characteristics of wave propagation and energy distributions in cylindrical elastic shells filled with fluid

The dispersion behaviour and energy distributions of free waves in thin walled cylindrical elastic shells filled with fluid are investigated. Dispersion curves are presented for a range of parameters and the behaviour of individual branches is explained. A non-dimensional equation which determines the distribution of vibrational energy between the shell wall and the contained fluid is derived and its variation with frequency and material parameters is studied.     

Acoustic streaming with resonance gas oscillations in a cylindrical tube

Acoustic streaming accompanying acoustic resonance oscillations of gas in a tube is considered. The effect of both the Prandtl number and the wall loss on the velocity of acoustic streaming in a viscous heat-conducting medium is investigated. Expressions for the longitudinal and transverse components of the flow velocity are obtained.     

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.     

Sound radiation from a cylindrical transducer filled with an elastic medium

An approximate method is proposed for calculating the acoustic field produced by a finite-height cylindrical piezoceramic transducer with allowance for the radiation from the ends of its inner volume that is filled with an elastic medium characterized by an arbitrary Poisson’s ratio. Structural features of the transducer (the presence of a sealing compound and an inner baffle) are taken into account. Good agreement is obtained between calculations and experiment for two transducers (a short one with a height-to-radius ratio h/a≈1 and a long one with h/a≈3) whose inner cavities are filled with either water or foam plastic.     

Bubbles effect on sound dispersion in thin-walled tube with polymeric liquid and elastic central rod

The present study is devoted to the investigation of fine air bubbles effect on sound propagation in thin-walled elastic tube with compressible polymeric liquid and cylindrical elastic rod in the central part of the tube. The problem formulation and solution method follow the previous paper of the authors (S.P. Levitsky, R.M. Bergman, J. Haddad, Sound dispersion in deformable tube with polymeric liquid and elastic central rod, Journal of Sound and Vibration 275 (1-2) (2004) 267-281). In order to account for the bubbles' influence on sound dispersion and attenuation, dynamic equation of state of the mixture, formulated within homogeneous approximation, is used. It is assumed that the volume gas concentration is small. The resulting dispersion equation for the waveguide with viscoelastic liquid-gas mixture is studied in a long-wave range. Results of simulations illustrate the influence of free gas concentration, bubble radius and rheological properties of the liquid on sound dispersion and attenuation in the system.     

Acoustic waves in thin-walled elastic tube with polymeric solution

Acoustic waves in a pipe with polymeric liquid are investigated within a quasi-one-dimensional approach. Analysis of the dispersion equation has shown that rheological features lead to essential changes in both attenuation and speed of the sound. The results may find application in acoustic rheometry of polymeric liquids and for modeling of fast dynamic processes in polymer production technology.     

Theoretical analysis of a relativistic travelling wave tube filled with plasma

A cold and uniform plasma-filled travelling wave tube with sinusoidally corrugated slow wave structure is driven by a finite thick annular intense relativistic electron beam with the entire system immersed in a strong longitudinal magnetic field. By means of the linear field theory, the dispersion relation for the relativistic travelling wave tube (RTWT) is derived. By numerical computation, the dispersion characteristics of the RTWT are analysed in different cases of various geometric parameters of the slow wave structure and plasma densities. Also the gain versus frequency for three different plasma densities and the peak gain of the tube versus plasma density are analysed. Some useful results are obtained on the basis of the discussion.     

Properties of surface waves in an elastic cylinder filled with a liquid

The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide.     

Modification of the boundary layer theory for analysis of wave motions in a cylindrical jet of a viscous liquid

The existent concepts of the boundary layer near the free surface of a viscous liquid, which is related to its periodic motion, are modified with the aim of analyzing the finite-amplitude wave motion on the surface of a thick charged jet of a viscous conducting liquid. To describe the flow in the boundary layer, a model problem is proposed that is simpler in statement compared with the complete problem and the solution of which uses the governing properties of the exact solution obtained in the low-viscosity asymptotics: the form of the dispersion relation, wave profile, and rate of velocity field viscous damping with time. An estimate is made of the boundary layer thickness at which the discrepancy between the exact solution and solution to the model problem (stated in terms of the theory proposed) falls into a given interval in the low-viscosity asymptotics. The domain of applicability of the modified theory is determined.     

Stability of steady rotation of a rotor partly filled with a viscous floating liquid

The problem of low-speed stability of steady rotation of a rotor with a cylindrical cavity partly filled with a viscous incompressible floating liquid is considered. The resultant force exerted by the liquid on the rotor performing small-radius circular precession is determined. The D-partition into regions with different degrees of instability of the plane of parameters of viscoelastic fixations of the rotor axis is constructed.     

Propagation of elastic wave in nanoporous material with distributed cylindrical nanoholes

The effective propagation constants of plane longitudinal and shear waves in nanoporous material with random distributed parallel cylindrical nanoholes are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is used to obtain the scattering waves from the single nanohole. The multiple scattering effects are taken into consideration by summing the scat- tered waves from all scatterers and performing the configuration averaging of random distributed scatterers. The effective propagation constants of coherent waves along with the associated dynamic effective elastic modulus are numerically evaluat- ed. The influences of surface stress are discussed based on the numerical results.     

Resonance theory of elastic wave scattering from a cylindrical cavity

Resonant excitation of a fluid-filled cylindrical cavity in an elastic medium by an incident compressional wave is investigated on the basis of the resonance theory of nuclear scattering. It is shown that the scattering amplitude consists of a series of narrow resonances super-imposed upon, and interfering with, a broad background that corresponds to the scattering from an empty cavity. The resonances may be analyzed in a most enlightening fashion by studying them separately in each partial wave of the normal-mode series. They are seen to correspond to excitations of the eigenvibrations of the cavity fluid caused by a phase-match of “creeping waves”, similar to the “Regge poles” of nuclear physics.