Numerical analysis of the dispersion of electroelastic waves in a cylinder whose physical properties have a longitudinal axis of symmetry

We develop a numerical method of analyzing the dispersion of electroelastic waves in a hollow circular cylinder. The method is based on the reduction of the wave problem to a spectral problem for a system of ordinary differential equations. This system is solved numerically. The roots of the dispersion equation are determined by the method of bisection. The practical convergence of the algorithm is shown using a specific example. One figure. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 151–156.     

Numerical analysis of the dispersion of acoustoelectric waves in a layer with a thickness axis of symmetry for its physical propertes

A numerical method is developed for studying normal electroelastic waves in a layer of piezoelectric materials with mm2 rhombic symmetry, and a second order thickness atris of symmetry. The main system of equations is reduced to eight hamiltonian-type equations in the thickness coordinate. For harmonic waves, the generalized spectral problem is solved numerically taking into account the even (odd) character of the solution with respect to the central plane of the layer. Some solutions of specific problems are analyzed. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 162–169, 1999.     

Surface and normal electroelastic shear waves in even-layered structures

We construct the dispersion equations for surface and normal shear waves propagating in layered periodic structures consisting of alternating layers of piezoelectric and metal. We carry out a numerical analysis of the equations obtained in a wide range of variation of frequency. We describe the distinctive characteristics of dispersion spectra of surface and normal waves and their interrelation. We give the characteristic distributions of the amplitude walues of the mechanical displacements and stresses and the electric potential. Three figures. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 50–58, 1991.     

A numerical-analytic method of studying the dispersion of elastic waves in a fixed orthotropic cylinder with a simply connected curvilinear section

We give a method of constructing the dispersion equations for waveguides made of recitilinearly orthotropic materials and having a section that is either elliptic or approximately that of a regular 2n-gon (n>-2) with rounded corners. The equations of motion for the waveguide can be integrated in series of basic particular solutions of exponential type. The dispersion functions are obtained in the form of reduced infinite determinants from homogeneous functional boundary conditions on the lateral surface of the waveguide after these conditions have been algebraized using orthogonal series expansions. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 97–102.     

Trapping waves by a submerged cylinder

For large values of the wavenumber k in the direction of cylinder, there is only one trapped wave. We construct asymptotics of these trapped modes and their frequencies as k → ∞ in the case of one submerged cylinder into a plane water layer by means of reducing the initial problem to three integral equations on the boundaries and then solving them using a method suggested by Zhevandrov and Merzon (Amer. Math. Soc. Translations (2) 208, 235–284 (2003)).     

Propagation of three-dimensional electroelastic shear waves in a regularly layered medium of metal-piezoelectric type

We construct and study the dispersion equations for electroelastic three-dimensional shear waves propagating in a periodic medium formed by alternating layers of conducting and piezoelectric materials. We determine the structure of the transmission and blocking zones (the spectral regions of stability and instability) for various relations among the parameters of the layers with waves propagating along the interfaces between the layers. Two figures. Bibliography: 8 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 4–8.     

Numerical solution of the propagation problem of longitudinal elastic waves in an orthotropic hollow cylinder

Wave processes in an orthotropic cylinder are analyzed. Harmonic oscillations are considered for which the original problem is reduced to a system of ordinary differential equations. This system is solved by the numerically stable discrete-orthogonalization method. Discrete curves for specific problems are given.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 75–78, 1985.     

One-dimensional nonlinear motions in electroelastic solids: Characteristics and shock waves

The general balance laws and jump relations of the nonlinear electroelasticity of anisotropic dielectrics presented in a previous work are systematically used to characterize and classify infinitesimal discontinuities and electroelastic shocks that can propagate in a simplified one-dimensional model. In particular, the characteristic speeds are obtained, the thermodynamical behavior of weak electroelastic shocks is established, and a classification of electroelastic shocks is given when the material admits a quadratic energy (so-called neo-Hookean case). The Hugoniot jump equation plays the fundamental role in the second point while electric switch-on and switch-off shocks can be exhibited in the classification. The work paves the way for a fully three-dimensional study in anisotropic ferroelectrics and ceramics.     

Numerical analysis of the stability of drift waves

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostiki, pp. 265–269, Izd. Moskovskogo Universiteta, Moscow, 1990.     

Numerical analysis of anomalous quasi-three-dimensional electromagnetic field above a conducting cylinder in a stratified medium

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostika, pp. 153–162, Izd. Moskovskogo Universiteta, Moscow, 1990.     

Dispersion of elastic waves in the contact-impact problem of a long cylinder

Numerical dispersion of two-dimensional finite elements was studied. The outcome of the dispersion study was verified by the numerical and analytical solutions to the longitudinal impact of two long cylindrical bars. In accordance with the results of the dispersion analysis it was demonstrated that the quadratic elements showed better accuracy than the linear ones.     

Diffraction of impulsive elastic waves by a fluid cylinder

We consider the diffraction of impulsive SV waves by a fluid circular cylinder. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with some acoustic fluid. The line source, generating the incident pulse, is situated outside the cylinder parallel to its axis. We investigate the problem by the method of dual integral transformation as developed by Friedlander. The resulting integrals are evaluated approximately to obtain the short-time estimate of the motion near the wave front in the shadow zone of the elastic medium. We also interpret the approximate solution in terms of Keller’s geometrical theory of diffraction.     

Scattering of impulsive elastic waves b a fluid cylinder

We consider the scattering of impulsive sv waves by a fluid circular cylinder. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with some acoustic fluid. The line source, generating the incident pulse is situated outside the cylinder parallel to its axis. We investigate the problem by the method of dual integral transformation as developed by Friedlander. The resulting integrals are evaluated approximately to obtain the short time estimate of the motion near the wave-front in the illuminated region of the elastic medium. We also interpret the approximate solution in terms of geometrical optics.     

Asymptotic solutions for electromagnetic waves in a nonlinear optical cylinder

Interactions between electromagnetic waves and a cylinder with field-dependent permeability is considered. Asymptotic solutions which represent the solutions to modifications of the nonlinear Schrödinger equation are found, in particular, soliton solutions.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 1, pp. 84–91, January, 1996.     

Numerical analysis of near electromagnetic fields of a parabolic cylinder and a paraboloid of revolution

Translated from Chislennye Metody Resheniya Obratnykh Zadach Matematicheskoi Fiziki, pp. 119–127.     

Transition waves and nonlinear interactions in the near wake of a circular cylinder

Transition waves and interactions between two kinds of instability—vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000–10 000 are studied by a domain decomposition hybrid numerical method. Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency, i.e.f _t /f_s∼Re^0.87 are obtained. The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza s prediction and some early experimental resultsf _t/f_s∼Re ^0.5 given by Blooret al. The multi-interactions between two kinds of vortex are clearly visualized numerically. The strong nonlinear interactions between the two independent frequencies (f _t,f _s ) leading to spectra broadening to form the couplingmf _s +nf _t are predicted and analyzed numerically, and the characteristics of the transition are described. Longitudinal variations of the transition wave and its coupling are reported. Detailed mechanism of the flow transition in the near wake before occurrence of the thedimensional evolution is provided. Project supported by the National Natural Science Foundation of China, the LNM of Institute of Mechanics, and partially by the National Basic Research Project.     

Propagation of torsional waves in a prestretched compound hollow circular cylinder

The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion curves are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 103–116, January–February, 2008.     

Numerical analysis of longitudinal elastic-plastic waves with radial effects

Summary The two-dimensional problem of longitudinal elastic-plastic waves in circular rods taking radial-inertia effects into account is solved based on the finite-element method and an explicit integration algorithm. The elastic-plastic constitutive equations are the yield criterion of von Mises with isotropic work hardening and the Prandtl-Reuss flow rule. Numerical results are shown for the region near the impact end of a semi-infinite rod for two sets of boundary conditions, namely prescribed longitudinal velocity and prescribed longitudinal stress at the bar end. The lateral motion of the struck end is assumed to be unrestrained (zero shear stress).The numerical results show response characteristics which deviate from the one-dimensional solution and which are in a good qualitative agreement with a number of experimental observations reported in the literature. These impact test results have been examined with respect to the predictions in order to separate radial- and strain-rate effects. Several specific calculations for the various test conditions have been performed to obtain quantitative agreement with experimental observations.

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Zusammenfassung Das zweidimensionale Problem der elastisch-plastischen Längswellen in kreisförmigen Stäben unter Berücksichtigung der Querschwingungen wird mit Hilfe der finiten Elemente und eines expliziten Integrationsalgorithmus gelöst. Als Materialgleichungen wurden die von Misessche Fliebedingung und das Fliegesetz nach Prandtl-Reuss verwendet. Für den halbunendlichen Stab werden numerische Resultate fur den Bereich des belasteten Endes gezeigt, wobei entweder die Geschwindigkeit oder die Spannung am belasteten Ende vorgegeben ist. Zusätzlich wird angenommen, da sich das Stabende in der Querrichtung frei bewegen kann.Die numerischen Resultate zeigen abweichend von der eindimensionalen Lösung Details, die gut mit einigen in der Literatur beschriebenen experimentellen Beobachtungen übereinstimmen. Diese Versuchsergebnisse wurden den numerischen Resultaten gegenübergestellt, um so den Einflu der Querschwingungen vom Einflu der Dehnungsgeschwindigkeit zu trennen. Um eine quantitative Übereinstimmung mit den experimentellen Beobachtungen zu erzielen, wurden einige Rechnungen mit den Versuchbedingungen als Eingabewerte durchgeführt.

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This paper is based on the doctoral dissertation of first author's dissertation at the Swiss Federal Institue of Technology (ETH), Zürich, Switzerland.     

The scattering of electromagnetic waves by a perfectly conducting infinite cylinder

We consider the scattering of a plane time-harmonic electromagnetic wave by a perfectly conducting infinite cylinder with axis in the direction k , where k is the unit vector along the z axis. Suppose the incident wave propagates in a direction perpendicular to the cylinder. For a given observation angle θ, let F_D(θ, α) k be the far-field pattern of the electric field corresponding to an incident wave with direction angle α polarized perpendicular to the axis and let F_N(θ; α) k be the far-field pattern of the magnetic field corresponding to an incident wave with direction angle α polarized parallel to the z axis. Let {α_n}_n=1^∞ be a distinct set of angles in [ ? π, π] and μ a complex number. Then, necessary and sufficient conditions are given for the set {(1 ? μ)F_D(θ;α_n) + μF_N(θ;α_n)}_{n = 1}^∞ to be complete in L²[ ? π, π]. Applications, together with numerical examples, are given to the inverse scattering problem of determining the shape of the cylinder from a knowledge of the far-field data.