Shock-wave propagation in an elastic rod with a viscoplastic external resistance

The wave problem of perturbation propagation along an elastic rod interacting with the medium is investigated using the model of viscoplastic friction. An exact solution of the problem is obtained for an arbitrary time of the loading period. Analysis of the results is performed.     

On wave propagation in inhomogeneous elastic media

Wave propagation in an inhomogeneous elastic rod or slab is considered. The governing equations are written in a matrix form and transformations are sought which reduce the system to a form associated with the wave equation. Integration of the system is then immediate. It is shown that such reduction may be achieved subject to a function involving the density and elastic parameters of the material adopting certain multi-parameter forms. These parameters are available for fitting to the behaviour of a variety of inhomogeneous elastic materials. A specific initial boundary value problem is solved by utilising the present method.     

Sound propagation and self-focusing in an inhomogeneous gas-liquid medium

The evolution of sound waves in a gas—liquid medium with an inhomogeneous distribution of the sound speed is considered in this paper on the basis of a nonlinear parabolic equation for the amplitude of the sound wave envelope. It is assumed that the nonlinearity due to the gas inclusions is much greater than the customary hydrodynamic nonlinearity. The influence of the inhomogeneity on the self-focusing of the sound is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 177–180, November–December, 1974.The author is grateful to I. R. Shreiber for discussion.     

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。     

On the propagation of elastic waves in a multiperiodically reinforced medium

By a multiperiodically reinforced medium (multiperiodic composite) we mean a composite in which the matrix material is reinforced by two or more families of periodically spaced fibres. Moreover, at least along one direction the periods corresponding to different families are different. An example of this composite is shown in Fig. 1, where along the x ¹-axis we deal with two different periods . The aim of the contribution is twofold. First, we propose a macroscopic (averaged) model of a multiperiodic composite, describing the effect of period lengths on the overall dynamic behaviour of the medium, in contrast to the known homogenized models. Second, we apply this model to the analysis of elastic waves propagating across a composite reinforced by two pairs of families of parallel periodically spaced fibres with different periods along certain direction.     

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     

Modeling of plane-wave propagation in an anisotropic elastic medium

We propose an algorithm that reduces the process of numerical solution to successive calculation of elementary one-dimensional problems of the type of a system of acoustic equations. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 199–206, January–February, 1999.     

The parameter perturbation method on elastic wave equation in inhomogeneous medium

I.IntroductionTheelasticwaveininhomogeneousmediumiscomplicatedbecauseofthediffracting,scattering,andtransmutingofthewavetapes.Exceptforsomesimpleandregularmediummode1s,thesolutionofelasticwavehasnotbeengotyet.Nowadays,theresearchoftheelasticwavescattering…     

Acoustics of stochastically inhomogeneous,deformable media

S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 10, pp. 109–115, October, 1993.     

Transient elastic wave propagation in a spherically symmetric bimaterial medium modeling the thorax

The transient response resulting from an impact wave on an elastic bimaterial, made out of a “hard” medium and a “soft” medium, welded at a spherical interface, have been investigated by using an integral transform technique. This technique permits isolation of the pressure and shear waves contributions to the wave field. The method of solution makes use of the generalized ray/Cagniard-de Hoop (GR/CdH) method associated with a “flattening approximation” (FA) technique, similar to the Earth flattening transformation used in geophysics. The GR/CdH method and the FA technique are briefly presented, together with their numerical implementations. The FA has proved to be useful in geophysical application, however, as far as the authors know, it has never been investigated for other applications. For the purpose of this paper, numerous tests of the method have been performed in order to check that the FA is appropriate to compute transient responses in the special case presented here. We could determine appropriate values for some parameters involved in the FA. This paper follows Grimal et al. [Int. J. Solid Struct. 39 (2002) 5345] in which we investigated the same bimaterial with a plane––instead of spherical––interface. Numerical examples are concerned with the propagation of an impact wave in the thorax modeled as a bimaterial (thoracic wall-lung). In addition to the effects of the weak coupling of the two media already observed in our previous study, we found that, for interface curvatures characteristic of those measured in the thorax, focalization of energy is manifest.     

Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium

The differential equations governing transfer and stiffness matrices and acoustic impedance for a functionally graded generally anisotropic magneto-electro-elastic medium have been obtained. It is shown that the transfer matrix satisfies a linear 1st order matrix differential equation, while the stiffness matrix satisfies a nonlinear Riccati equation. For a thin nonhomogeneous layer, approximate solutions with different levels of accuracy have been formulated in the form of a transfer matrix using a geometrical integration in the form of a Magnus expansion. This integration method preserves qualitative features of the exact solution of the differential equation, in particular energy conservation. The wave propagation solution for a thick layer or a multilayered structure of inhomogeneous layers is obtained recursively from the thin layer solutions. Since the transfer matrix solution becomes computationally unstable with increase of frequency or layer thickness, we reformulate the solution in the form of a stable stiffness-matrix solution which is obtained from the relation of the stiffness matrices to the transfer matrices. Using an efficient recursive algorithm, the stiffness matrices of the thin nonhomogeneous layer are combined to obtain the total stiffness matrix for an arbitrary functionally graded multilayered system. It is shown that the round-off error for the stiffness-matrix recursive algorithm is higher than that for the transfer matrices. To optimize the recursive procedure, a computationally stable hybrid method is proposed which first starts the recursive computation with the transfer matrices and then, as the thickness increases, transits to the stiffness matrix recursive algorithm. Numerical results show this solution to be stable and efficient. As an application example, we calculate the surface wave velocity dispersion for a functionally graded coating on a semispace.     

Shock-wave propagation through a vertical foam column with a density gradient

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 27–32, March–April, 1992.