Propagation of waves along a slightly bent piezoelectric rod

The waveguide modes of a curved piezoelectric rod are considered. The propagation of waves along the rod is studied by the ray method. The transport equations that describe the change in the intensity along the rays are solved. Bibliography:10 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 191–202. Translated by V. V. Lukyanov     

Propagation of Scholte-Gogoladze surface waves along a curved fluid-solid interface

A high-frequency ray theory is presented for a type of small-amplitude waves (termed Scholte-Gogoladze waves), localized in a thin layer around an interface between elastic and fluid domains. The interface is assumed to be smooth, with typical radii of curvature much larger than the excitation wavelength. The technique employed in the paper is based on a boundary-layer version of the classical WKB-expansion (see V. M. Babich and N. Ya. Kirpichnikova, The Boundary-Layer Method in Diffraction Problems (Springer, Berlin 1979)). Bibliography: 20 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 229–246.     

Propagation of elastic waves along the fibers in oriented glass-reinforced plastics

The dispersion equation is derived for axisymmetric (longitudinal and torsional) normal vibrations in oriented glass-reinforced plastics. The low-frequency case is examined in detail. The frequency limits of applicability of the method of substituting a homogeneous medium for the composite (GRP) are estimated. The dependence of the vibration propagation velocity on glass content is calculated.Leningrad Zonal Scientific-Research Institute of Experimental Design of Public and Residential Buildings. Translated from Mekhanika Polimerov, No. 6, pp. 976–983, November–December, 1973.     

Propagation of sound in a duct with mean flow

We have considered the problem of radiation of sound from a semi-infinite soft duct. This duct is symmetrically located inside a hard but infinite duct. The problem is solved when the whole fluid region inside these ducts is in motion with a constant fluid velocity. We obtained a closed form solution by using the integral transform and Wiener–Hopf technique. The graphical results are also presented which show that how effectively the unwanted noise can be reduced by proper selection of different parameters.     

Couette flow of a stratified fluid with suction varying along a boundary

A viscous incompressible fluid between two plane boundaries is stratified by maintaining the planes at different temperatures. The upper plane moves with a uniform velocity. The suction/injection mechanism with constant injection velocity at the upper plane and suction velocity varying sinusoidally along the lower plane with a wave numberk is introduced at the boundaries. The steady linearised equations are solved using similarity variables for the velocity components. The wave numberk is shown to be effective in controlling the boundary layer thickness.     

Propagation of TM waves in a layer with arbitrary nonlinearity

A boundary value problem for Maxwell’s equations describing propagation of TM waves in a nonlinear dielectric layer with arbitrary nonlinearity is considered. The layer is located between two linear semi-infinite media. The problem is reduced to a nonlinear boundary eigenvalue problem for a system of second-order nonlinear ordinary differential equations. A dispersion equation for the eigenvalues of the problem (propagation constants) is derived. For a given nonlinearity function, the dispersion equation can be studied both analytically and numerically. A sufficient condition for the existence of at least one eigenvalue is formulated.     

Propagation of internal waves in a three-layer liquid

The propagation o f internal harmonic waves in a three-layer liquid is examined in a linear approximation for arbitrary wave numbers. A travelling wave sohaion is obtained and a dispersion equation is derived. The roots of the dispersion equation and the dependence of the solution on the ratio of the densities of the liquids are examined in detail. The phase and group velocities are plotted as functions of wavelength and graphs of the various wave modes are presented. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 170–174, 1999.     

Propagation of shear waves in a semi-infinite elastic waveguide with a local constriction

A procedure is proposed for computing longitudinal-shear stresses and displacements in a semi-infinite waveguide with two lateral cutouts. Numerical results are reported for the stresses on the cutout contours and for the transmission coefficient of the elastic wave.Sumy Branch, Khar'kov Polytechnical Institute. Translated from Dinamicheskie Sistemy, No. 10, pp. 14–20, 1992.     

Propagation of localized bending deformations in microtubules

A continuum medium model is proposed describing a microtubule (MT) as an elastic rod. When the MT is subjected to a constant bending force, the dynamics of the angular deviation, with respect to the MT's rectilinear configuration, is governed by a Sine-Gordon equation. Particular analytical solutions are kink and anti-kink bending modes which may propagate at various speeds along the MT's length. Kinetic energies of these modes compare with thermal and ATP hydrolysis energies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of thermoelastic Rayleigh waves in a solid underlying a fluid layer with varying temperature

The present paper is aimed at to study the propagation of surface waves in a homogeneous isotropic, thermally conducting and elastic solid underlying a layer of viscous liquid with finite thickness in the context of generalized theories of thermoelasticity. The secular equations for non-leaky Rayleigh waves, in compact form are derived after developing the mathematical model. The amplitude ratios of displacements and temperature change in both media at the surface (interface) are also obtained. The liquid layer has successfully been modeled as thermal load in addition to normal (hydrostatic pressure) one, which is the distinctive feature of the present study and missing in earlier researches. Finally, the numerical solution is carried out for aluminum-epoxy composite material solid (half-space) underlying a viscous liquid layer of finite thickness. The computer simulated results for dispersion curves, attenuation coefficient profiles, amplitude ratios of surface displacements and temperature change have been presented graphically, in order to illustrate and compare the theoretical results. The present analysis can be utilized in electronics and navigation applications in addition to surface acoustic wave (SAW) devices.     

Propagation of longitudinal viscoelastic waves in a three-layer medium

The nonstationary problem of propagation of a longitudinal plane one-dimensional stress wave through a plane-parallel viscoelastic layer of finite thickness separating two linear elastic half-spaces with different properties is solved in the linear formulation. A plane wave traveling in one of the half-spaces is normally incident on the boundary of the layer (one-dimensional problem). The field in the other elastic half-space, excited as a result of the multiple reflection of the fronts from the boundaries of the layer, is investigated. Graphs of the small displacements at a given point of the elastic half-space are presented. The solution of the problem is based on the dynamic correspondence principle formulated by Bland [3].Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 151–156, January–February, 1971.     

Propagation of stationary waves in a compound deformable tube filled with a viscous liquid

The problem of modeling the motion of the blood in a large vessel, partly replaced by a prosthesis (or graft) is considered. It is assumed that the material of the vessel and prosthesis is represented by a Voigt linear viscoelastic model.S. M. Kirov Azerbaidzhan State University, Baku. Translated from Mekhanika Polimerov, No. 1, pp. 175–178, January–February, 1976.     

A note on a WKB application to a duct of varying cross-section

In this paper, the two-dimensional problem of an incident plane sound wave traveling along a rigid duct or a rigid horn is studied. It has been shown that a simple one-dimensional analysis gives accurate predictions of the sound propagation. The impedance of a particular horn is obtained using the Wentzel-Kramers-Brillouin (WKB) approximation to solve the Webster equation. The mouth of the horn is assumed to be terminated in an infinite baffle. Computation of the normalized acoustic impedance using the WKB approach shows less floating point operations when compared with a Runge-Kutta algorithm.     

Propagation of acoustic waves in a fibrous fluid-filled material

The homogenization method is used for the analysis of acoustic wave propagation in a unidirectional fibrous material for the acoustic control of the fiber arrangement in manufacturing composites. Acoustic equations for a rigid periodic structure filled by a nonviscous fluid are obtained by two-dimensional asymptotic expansions. A regular square and triangular arrangement of the fibers with a round cross-section are considered. The analysis reveals that the velocity of acoustic waves is significantly affected by both the volume content and the fiber arrangement.Moscow State Academy of Chemical Engineering, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 651–655 September–October, 1997.     

Propagation of electromagnetic waves in a nonlinear dielectric slab

The early phases of propagation of a large amplitude electromagnetic disturbance in a nonlinear dielectric slab embedded between two linear media are investigated by the method of characteristics. This disturbance is triggered by the arrival of an electromagnetic shock wave at one of the interfaces. Reflection and transmission of an arbitrary signal when it arrives at one of the slab boundaries is characterized in terms of nonlinear reflection and transmission coefficients for the interface. No restrictions are placed on the form of the constitutive laws of the material comprising the slab. By introducing, for the nonlinear dielectric, a class of model equations, an exact solution to the characteristic equations which describes the interaction of a centered wave with anarbitrary oncoming signal is obtained. Solutions for the electromagnetic fields are derived for the special case in which the incident disturbance interacts with the reflected signal from the slab interface. A particular case of the disturbance propagating across a nonmagnetic slab is also examined.     

Propagation of torsional waves in a circular elastic rod

Zusammenfassung Das Problem eines unendlichen kreiszylindrischen Halbstabes, dessen Endquerschnitt mit beliebigen Torsionsspannungen belastet ist, wird auf Grund der strengen dreidimensionalen Elastizitätstheorie gelöst. Die Lösungsmethode besteht aus einer Integraltransformationstechnik mit asymptotischer Inversion für eine frequenzmodulierte Stufenfunktion. Die Ergebnisse zeigen, dass die Gültigkeit eines «dynamischen Saint-Venant-Prinzips» von der betreffenden Frequenzkomponente abhängt.

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This work was initiated while the author was still employed by the IBM Corp. at Endicott, New York.