Sound and weak shock wave propagation in gas-liquid foams

Propagation of sound and weak shock waves in gas-liquid foams is investigated theoretically and experimentally. An original physical model is developed to describe the evolution of small perturbations in a foam of polyhedral structure. The model developed takes into account both peculiarities of interface heat transfer in foam and liquid motion through the system of Plateau-Gibbs borders which results in the appearance of an additional hydrodynamic dissipative force. The Rayleigh equation analog, which takes into account the latter phenomenon, is obtained. Structure and dynamics of weak shock waves are investigated. A vertical shock tube was constructed and used to measure the parameters of weak shock wave propagation in gas-liquid foams of polyhedral structure. Spectral analysis of the data obtained shows that there are weak dispersion and strong dissipation of the initial signal. Comparison of the evolution of experimental and theoretical profiles permits to conclude that the suggested model allows to describe the peculiarities of acoustical perturbations in gas-liquid foam more precisely than it follows from the standard models. Received 15 September 1993 / Accepted 27 December 1993     

非均匀吸收介质中地震波的广义传播矩阵解法

本文在复频域内,通过应用混合变量粘弹性波方程和线性常微分方程组的指数矩阵解法,给出了一种计算非均匀吸收介质中地震波传播的广义传播矩阵解法。该方法适用于各种粘弹性模型,可模拟任意震源及所产生的各种体波、面波,数值结果表明具有很高的计算精度。     

Propagation of nonlinear waves in an inhomogeneous gas-liquid medium. Derivation of wave equations in the Korteweg-de Vries approximation

Equations describing the propagation of waves of small but finite amplitude in a liquid with gas bubbles are derived. The bubble distribution density is a continuous function of bubble size and spatial coordinates. It is found that, for a uniform bubble distribution, the obtained equations become the Korteweg-de Vries, Kadomtsev-Petviashvili and Khokhlov-Zabolotskaya equations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 188–197, March–April, 2009.     

Swell wave propagation in an inhomogeneous ice sheet

The propagation of surface waves beneath a periodically inhomogeneous ice sheet is considered. Areas of broken ice and hummock ridges are considered as irregularities. It is shown that waves with frequencies corresponding to wind and swell waves are strongly scattered by the irregularities and are damped exponentially as they propagate beneath the ice.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 162–169, September–October, 1996.     

Sound propagation through a discretely inhomogeneous thermoelastic plane layer adjacent to heat-conducting liquids

An analytical solution of the problem of the propagation of a plane sound wave through a discretely inhomogeneous thermoelastic layer adjacent to inviscid heat-conducting liquids is obtained. Results of calculations of the dependences of the transmission coefficient on the wave incidence angle and frequency for discretely inhomogeneous and continuously inhomogeneous thermoelastic layers are given. It is shown that a thermoelastic layer with continuously inhomogeneous thickness can be simulated using a system of homogeneous thermoelastic layers.     

Percolation model of an inhomogeneous anisotropic medium

A model of the variation in capillary conductivity is proposed. The change in the permeability of an inhomogeneous medium under load is investigated on the basis of the percolation model [3] and is numerically modeled for cases of hydrostatic compression and nonisotropic loading. The validity of the percolation approach to the determination of the change in flow properties under load is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 67–75, January–February, 1986.     

Wave propagation in an initially stressed hypo-elastic medium

The complete integration of the growth equation of the wave for an initially stressed hypo-elastic medium is given. The main result is that the growth now depends on the normal to the wave front. Explicit construction is given for a body of grad one and the results illustrated for one of grad zero.     

Effective elastic moduli of an inhomogeneous medium with cracks

In the present paper, the effective elastic moduli of an inhomogeneous medium with cracks are derived and obtained by taking into account its microstructural properties which involve the shape, size and distribution of cracks and the interaction between cracks. Numerical results for the periodic microstructure of different dimensions are presented. From the results obtained, it can be found that the distribution of cracks has a significant effect on the effective elastic moduli of the material. The project supported by the National Education Committee for Doctor     

Thermoelastic wave propagation in inhomogeneous media

Summary A novel approach to the modeling of thermoelastic wave propagation is presented, based on the thermodynamics of discrete systems. The first novelty includes the representation of integral balance laws for thermoelasticity in terms of contact quantities that describe the nonequilibrium state of elements. The next new aspect is a modification of the recently proposed wave-propagation algorithm, which is used as a tool for determining the contact quantities in a finite-volume scheme for the numerical simulation of two-dimensional thermoelastic wave propagation in inhomogeneous media. Such a modification is needed to provide the satisfaction of the thermodynamic consistency conditions between adjacent discrete elements. Results of computations for certain test problems show the efficiency and physical consistency of the algorithm. Received 11 November 1999; accepted for publication 2 May 2000     

Shock wave in a gas-liquid medium

The propagation of weak shock waves and the conditions for their existence in a gas-liquid medium are studied in [1]. The article [2] is devoted to an examination of powerful shock waves in liquids containing gas bubbles. The possibility of the existence in such a medium of a shock wave having an oscillatory pressure profile at the front is demonstrated in [3] based on the general results of nonlinear wave dynamics. It is shown in [4, 5] that a shock wave in a gas-liquid mixture actually has a profile having an oscillating pressure. The drawback of [3–5] is the necessity of postulating the existence of the shock waves. This is connected with the absence of a direct calculation of the dissipative effects in the fundamental equations. The present article is devoted to the theoretical and experimental study of the structure of a shock wave in a gas-liquid medium. It is shown, within the framework of a homogeneous biphasic model, that the structure of the shock wave can be studied on the basis of the Burgers-Korteweg-de Vries equation. The results of piezoelectric measurements of the pressure profile along the shock wave front agree qualitatively with the theoretical representations of the structure of the shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 65–69, May–June, 1973.     

SH waves due to a point source in an inhomogeneous medium

The propagation of SH waves due to a point source in an homogeneous medium lying over an inhomogeneous substratum has been investigated in this paper. The Green's function technique developed by Ghosh has been used to solve the problem.