Wave propagation in an elastic layer with voids located in a liquid

We obtain the dispersion equations that describe the propagation of waves in an elastic layer with voids locted between two liquid half-spaces. We study certain limiting cases corresponding to the absence of voids or liquid. We obtain the roots of the dispersion equations for both dissipative and nondissipative systems. It is shown that the relation of the real part of the phase velocity to the wave number in a dissipative system is qualitatively similar to the corresponding relation for the real value of the phase velocity in the case when dissipation is absent. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 90–96.     

Wave propagation in thermo-chiral elastic medium

The propagation of time harmonic waves through an infinite thermo-chiral elastic material has been investigated. The elastic field of thermo-chiral medium has been described by extending the governing equations and constitutive relations of hemitropic micropolar material to include temperature field. Seven basic waves consisting of three coupled dilatational waves and four coupled shear waves traveling with distinct speeds may exist in the medium. All the waves are found to be dispersive, however the coupled dilatational waves are attenuating and temperature dependent, while the coupled shear waves are independent of temperature field. The phase speeds and corresponding attenuation quality factors of all the coupled dilatational waves have been computed numerically for a specific model. The effect of chirality and temperature field have been shown graphically.     

Wave propagation through a 2D lattice

Nonlinear wave propagation through a 2D lattice is investigated. Using reductive perturbation method, we show that this can be described by Kadomtsev–Petviashvili (KP) equation for quadratic nonlinearity and modified KP equation for cubic nonlinearity, respectively. With quadratic and cubic nonlinearities together, the system is governed by an integro-differential equation. We have also checked the integrability of these equations using singularity analysis and obtained solitary wave solutions.     

Wave propagation in nonlocal elastic continua modelled by a fractional calculus approach

In the present paper, the wave propagation in one-dimensional elastic continua, characterized by nonlocal interactions modeled by fractional calculus, is investigated. Spatial derivatives of non-integer order 1 < α < 2 are involved in the governing equation, which is solved by fractional finite differences. The influence of long-range interactions is then analyzed as α varies: the resonant frequencies and the standing waves of a nonlocal bar are evaluated and the deviations from the classical (local) ones, recovered by imposing α = 2, are discussed.     

Wave propagation in a mixed convection boundary‐layer over a horizontal surface

The propagation of disturbances in a mixed convection boundary‐layer flow over a horizontal plate is described by a triple deck problem in the case of the buoyancy parameter being small. The pressure correction in the lower deck consists of two parts: One due to the buoyancy effects in the main deck and one due to the displacement of the outer flow field. The response of the boundary layer flow to an oscillator of frequency ω will be computed and upstream travelling waves will be identified.     

P-wave propagation through elastic solids with a doubly periodic array of cracks

An analytical approach to study normal penetration of a longitudinalplane wave into a doubly periodic array of slit-type obstaclesis developed. By means of suitable assumptions on the physicaland geometrical parameters we arrive at explicit formulae forthe relevant scattering parameters and fields. The underlyingcontext is wave propagation through damaged (elastic) solids.Figures are given which reflect the peculiarities of propagationin such a structure     

Wave propagation in,layered, transversally isotropic,elastic media

Wave propagation in a transversally isotropic, elastic medium consisting of plane-parallel layers and half spaces is considered. A generalized matrix method is used to derive the dispersion equation of this medium and to find the coefficients of reflection and refraction. This method makes it possible to consider dispersion curves and the coeffients of reflection and refraction in a broader domain than with Haskell's method. The results obtained generalize to layers in which the elastic characteristics vary with depth according to an arbitrary law. For such layers it is possible to find matrices in the form of series which converge rapidly for low and high frequencies. Moreover, a rule is formulated which makes it possible on the basis of a known field in an isotropic medium to find the field in the corresponding transversally isotropic medium.     

On wave propagation along a weakly laterally inhomogeneous, weakly bent anisotropic elastic layer

The propagation of a waveguide mode along a weakly bent elastic anisotropic layer is considered. Analytic expressions for the amplitude and the Berry phase of the corresponding oscillation are obtained.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 12–32.     

Surface wave propagation in a liquid-saturated porous solid layer lying over a heterogeneous elastic solid half-space

Dispersion equation is derived for the propagation of Rayleigh type surface waves in a liquid saturated porous solid layer lying over an inhomogeneous elastic solid half-space. Effect of heterogeneity on the phase velocity is studied by taking different numerical values of heterogeneity factor for particular models. Dispersion curves have been drawn showing the effect of heterogeneity on the phase velocity.     

Wave propagation in periodically layered elastic media based on an internal variable model

A phenomenological model of wave propagation in a periodically layered elastic media, with linear elastic constituents, which is based on an internal variable theory, is presented; the main result is a system of coupled second- and fourth-order partial differential equations which describe the motion of each constituent and which, in turn, appear to predict the correct qualitative behavior for both the composite (or main) wave and the precursor wave in the laminate.     

Wave propagation in a long polymer rod

The author examines the propagation of longitudinal waves in a semi-infinite rod whose material possesses elasticoviscous-plasticoviscous properties. Time conditions are introduced to take flow retardation into account, together with a hypothesis concerning the rate influence function. The Laplace transform method is used to obtain a solution close to the wave front; the solution for the plasticoviscous stage is obtained by a graphoanalytical method.Mekhanika Polimerov, Vol. 2, No. 2, pp. 253–262, 1966     

Wave propagation in an isolated porous Biot layer with closed pores on the boundaries

On the boundaries of such an isolated porous Biot layer, the total stresses and normal relative displacement are equal to zero. For this layer, the symmetric and antisymmetric dispersion equations are established and investigated. The wave field consists of normal waves. In this layer, one bending wave, two plate waves, and infinitely many normal waves propagate. For all these waves, we determine dispersion curves by analytical methods. The velocities of the bending wave and the second plate wave for the infinite frequency are equal to the Rayleigh velocity. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 173–189.     

The propagation of elastic waves in a piezoelectric

Formulas of the ray method are developed in the case of the propagation of high-frequency waves in a piezoelectric. It follows from the equations of the paper that in first approximation the energy of the wave field propagates along rays.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 155–161, 1974.     

Two-dimensional wave propagation in a generalized elastic solid

The object of the present study is to investigate the propagation of two-dimensional waves in a weakly nonlinear and weakly dispersive elastic solid. The reductive perturbation method is directly applied to a Lagrangian whose Euler–Lagrange equations give the field equations for a quadratically nonlinear elastic medium with higher order gradients. In the long-wave approximation, it is shown that the long-time behavior of the two transverse waves is governed by the two coupled modified Kadomtsev–Petviashvili (CMKP) equations. Depending on the choice of the direction of perpendicular dynamics, various forms of the CMKP equations are obtained. Some special solutions are also presented for a simplified form of the CMKP equations.     

Wave motions in a spatial boundary layer

The propagation of perturbations in a boundary layer under conditions when the velocity of the approaching stream may be both subsonic and supersonic is considered. With regard to the initial flow in the boundary layer it is assumed that it is stationary and possesses a spatial character which is caused by the external pressure gradient and not by the curvature of the body around which the flow occurs (boundary layers of this kind are extensively used in experiments at the present time). The linearized equations describing waves of vanishingly small amplitude are studied in detail. An analysis of the dispersion relation which links the frequency of the free oscillations with the components of the wave vector reveals a number of special features which are only present in motions with a three-dimensional velocity field. In particular, it is established that the Cauchy problem for the system of linear equations is ill-posed.     

Wave propagation in a fluid-saturated inhomogeneous porous medium

A closed system of constitutive equations for the dynamical and geometric quantities in a fluid- saturated inhomogeneous elastic porous medium is constructed within the framework of the three-dimensional theory of elasticity. The geometrical characteristics of the wave front and of the ray in a fluid-saturated inhomogeneous medium are obtained from the Fermi's principle.     

On the connection of the superposition and homogeneous-solutions methods in wave propagation problems in a semi-infinite rigidly-clamped elastic layer

The process of harmonic wave propagation is investigated in a semi-infinite rigidly-clamped elastic layer. An analytic solution of the problem is obtained by the superposition method. The wave field expansion in the form of a normal mode series for a corresponding infinite waveguide is established. According to residue theory, the explicit form of the expansion coefficients is established with physical requirements of the radiation conditions taken into account.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 3–10, 1988.     

Wave propagation in nonlinear media

The behavior of nonlinear dispersive or dissipative waves is analyzed using the decomposition method.