Signal velocity for transient waves in linear dissipative media

The aim of this paper is to discuss the concept of signal velocity for transient sinusoidal waves in linear dissipative media. The method of the steepest descent path, first introduced by Brillouin in this respect, is used to show whether the signal velocity may equal the group velocity or the phase velocity.     

Inhomogeneous waves in anisotropic dissipative bodies

Wave propagation in anisotropic dissipative bodies is considered through the form of inhomogeneous waves. The dissipativity of the body is characterized by a restriction of thermodynamic character on the viscoelastic tensor. As a consequence, the divergence of the usual (time-averaged) energy flux is proved to be negative. This in turn is shown to imply that the amplitude of the wave decays in the direction of the energy flux and the angle, subtended by the imaginary part of the wave vector and the energy flux, is acute. Moreover, the symmetry of the viscoelastic tensor and the positive definiteness of its real part imply that also the imaginary part of the wave vector subtends an acute angle with the energy flux. Such properties are shown to hold in both solids and fluids. Because of anisotropy, the angle subtended by the real and imaginary parts of the wave vector need not be acute, which means that the amplitude may increase in the direction of phase propagation.     

On the theory of plane inhomogeneous waves in anisotropic elastic media

In the theory of plane inhomogeneous elastic waves, the complex wave vector constituted by two real vectors in a given plane may be described with the aid of two complex scalar parameters. Either of those parameters may be taken as a free one in the characteristic condition assigned to the wave equation. This alternative underlies the two fundamental approaches in the theory, namely, one associated with the Stroh eigenvalue problem and the other with the generalized Christoffel eigenvalue problem. The two approaches are identical insofar as a partial nondegenerate wave solution (partial mode) is concerned, but they differ in the fundamental solution (wave packet) assembling, and their dissimilarity is also revealed in the presence of degeneracies, which may involve either of the two governing parameters or both of them. Therefore, use of both approaches is essential for studying the degeneracy phenomenon in the theory of inhomogeneous waves. The criteria for different types of degeneracy, related to a double eigenvalue of the Stroh matrix or the Christoffel matrix and at the same time to a repeated root of the characteristic condition, are formulated by appeal to the matrix algebra and to the theory of polynomial equations. On this basis, dimensions of the manifolds, associated with degeneracy of different types in the space of variables, are established for elastic media of unrestricted anisotropy. The relation to the boundary-value problems is discussed.     

Toward a theory of the propagation of elastoplastic waves in strain-hardening media

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 166–172, September–October, 1994.     

Propagation velocities of elastic waves in saturated soils

Based on the wave equations established by the authors, the characteristics of propagation velocities of elastic waves in saturated soils are analyzed and verified by ultrasonic test in laboratory and seismic survey in the field. The results provide theoretical basis for the determination of physical and mechanical parameters of saturated soils using propagation velocities of elastic waves, especially P-wave Velocity.     

Wave and shock velocities in relativistic magnetohydrodynamics compared with the speed of light

We prove that the natural thermodynamic restrictions on the constitutive equations in relativistic magnetohydrodynamics (stability of equilibrium state) are necessary and sufficient to guarantee that the normal and the radial velocity of the wave front of disturbances and the shock velocity do not exceed the light speed.     

Limit velocities of lamb waves: Analytic and numerical studies

The Lamb wave propagation in elastic isotropic and orthotropic layers is studied by numerical and analytic methods. An analytic solution is obtained by using the Cauchy formalism for the entire frequency range. Numerical solutions are obtained in a neighborhood of the second limit velocity corresponding to very small frequencies. The influence of variations in the layer geometry on the dispersion curves is studied.     

Measurement of particle velocities associated with waves propagating in bars

The measurement of longitudinal and radial particle velocities, associated with waves propagating in bars, by an electro-magnetic-induction method is described. It is shown that both velocity components can be measured in conducting and nonconducting bars with approximately the same order of precision normally achieved in strain measurements. Precautions which must be observed are discussed and typical results are presented.     

Dispersion and absorption of plane harmonic waves in a relativistic gas

Received October 10, 2000 / Published online June 1, 2001     

Elastic waves in crystals and anisotropic media

The results of investigation of propagation of elastic waves in anisotropic media are discussed taking into account the two-dimensional problem of a source in an infinite medium and the Lamb problem for a half-plane. The media considered in the investigation are those for which the equations of motion under plane deformation conditions are characterized by four constants.     

The dissipative mechanism in flowing polymers: theory and experiments

The application of modern non-linear continuum thermodynamics to the analysis of energy dissipation in both isothermal and non-isothermal flow of polymers is discussed. A fundamental simplification of the field equation for the balance of energy arises if the assumption is made that the flowing polymer is a material with entropic elasticity. This assumption is partly justified by structural arguments, and its validity can be checked experimentally. The results of the experiments performed support the validity of the assumption.     

Spherical blast waves in multicomponent media

The solution of the problem of propagation of a wave in soils is presented for the case when the wave is produced by the detonation of a spherical charge of some explosive material (EM). The solution is obtained on a computer by the method of characteristics. The soils are regarded as multicomponent media consisting of solid particles, water, and air in conformity with the model proposed in [1, 2]. The dependence of the pressure, velocity of the particles, and the density in the wave front on the distance is determined; the variation of these parameters with time at fixed points of the medium is also determined. The results are compared with the results of tests [1, 2]. Their close agreement for different contents of the components indicates the applicability of the multicomponent model to soils. The limits of applicability of the model are determined. The propagation of a plane wave under the same conditions was investigated in [3].