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1.
Summary A class of wave equations, derived by means of a Lagrangian density, is discussed. The dispersion relation W(, k)=0, where is the frequency and k the wave number of a harmonic wave has been derived and some properties of the functions 2(k 2) have been shown. Conservation laws have been derived, and formal solutions of the initial value problem and a class of mixed initial-boundary value problems have been presented. It has been shown that the solutions of the latter class are causal although the Kramers-Kronig relations are not satisfied.  相似文献   

2.
Within the framework of one-dimensional unsteady compressible flow in deformable pipes, the present work proposes expressions able to represent the stress state of a “fluid-pipe” continuous system. The coefficients needed to define the friction forces are calibrated against experimental results. The proposed expressions highlight the crucial role played by the fluid compressibility on the wave resistance.  相似文献   

3.
Summary Propagation of flexural waves in circularly cylindrical bars of anisotropic material on the basis of the exact three-dimensional theory of elasticity of small deformations is considered, the rigor of the analysis being the same as the one of the Pochhammer-Chree theory. A system of the governing equations of motion for the cylindrical orthotropy (its axis coinciding with the axis of the bar) is derived and expressed in terms of radial, tangential and axial displacement components. For a steady-state sinusoidal flexural wave the system reduces to coupled ordinary second order differential equations with a regular singular point. Solution for a transversely isotropic is obtained by means of Frobenius series method. Upon using two or three terms of the series approximate dispersion relations for isotropic material as well as for the pyrolytic graphite type material and two other types of anisotropic materials are obtained and illustrated by graphs. Higher order modes than those already known are found.
Übersicht Die Fortpflanzung von Biegewellen in kreiszylindrischen Balken aus anisotropem Material wird auf der Grundlage der exakten dreidimensionalen Elastizitätstheorie kleiner Verformungen betrachtet. Die Strenge der hier gegebenen Untersuchungen entspricht der in der Theorie von Pochhammer-Chree. Das System der Bewegungsgleichungen wird für zylindrische Orthotropie, deren Achse mit der Balkenachse zusammenfällt, abgeleitet und durch die radialen, atngentialen und axialen Verschiebungskomponenten ausgedrückt. Das System reduziert sich im Fall einer stationären sinusförmigen Biegewelle auf gekoppelte, gewöhnliche Differentialgleichungen 2. Ordnung mit einem singulären Punkt. Lösungen für transversale Isotropie werden mit Hilfe der Reihenmethode von Frobenius abgeleitet. Unter Verwendung von zwei oder drei Gliedern dieser Reihen werden angenäherte Dispersionsbeziehungen sowohl für isotropes Material als auch für Material vom Typ pyrolytischen Graphits und für zwei andere Typen anisotropischer Materialien erhalten und graphisch dargestellt. Es werden Schwingungsformen gefunden, die von höherer Ordnung als die bisher bekannten sind.


Research supported by a grant of the National Science Foundation.  相似文献   

4.
The effect of finite Hall dispersion on the propagation of linear waves is studied within the framework of isotropic magnetohydrodynamics. It is shown that the presence of finite dispersion does not lead to instability of the uniform plasma state. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 205–206, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 94-01-01383).  相似文献   

5.
Summary Some considerations have been given about the wave guiding properties of a cylindrical region of fluid of which the density and the velocity of sound differs from the surrounding fluid. The existence and the number of waves is discussed.  相似文献   

6.
The one-dimensional propagation of thermoelastic waves in isotropic homogeneous half spaces within the theory of Green and Lindsay [1] is studied. Padé-extended ray methods are employed to obtain the desired information. Comparisons between the predictions of the Green and Lindsay theory and the theory of Lord and Shulman [2] are made. Our ray series solutions show that for discontinuous thermal disturbances the displacement according to the Green and Lindsay theory is also discontinuous. This violates the fundamental continuum hypothesis that matter is impenetrable. For a simple numerical example we show also that a compressive behaviour in the displacement may be associated with a tensile behaviour in the stress and vice versa. This prediction of the Green and Lindsay theory is also unrealistic from the physical point of view.  相似文献   

7.
8.
M. P. Levin 《Fluid Dynamics》1996,31(6):865-867
The problem of the propagation of pressure waves through compressible porous media saturated with a slightly compressible fluid is considered. By using Darcy's law the problem is reduced to a mixed initial-boundary value problem for an equation of the heat conduction type with a nonlinear term. The method of quasi-characteristics is used to solve this equation numerically. Solutions of the wave propagation problem for media with different permeability coefficients are presented. A solution of the inverse problem of determining the permeability coefficient using wave-pulse test data is constructed on the basis of a set of solutions of the direct problem.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 81–84, November–December, 1996.  相似文献   

9.
Summary With the aid of an ultrasonic pulse technique, the propagation of elastic waves (longitudinal as well as transverse) through polyurethane rubbers filled with different amounts of sodium chloride particles was studied. The velocity of both longitudinal and transverse waves was found to increase with filler content. From the measured wave velocities, the effective modulus for longitudinal waves,L, bulk modulus,K, and shear modulus,G, were calculated according to the relations for a homogeneous isotropic material. All three moduli appear to be monotonously increasing functions of the filler content over the whole experimentally accessible temperature range (–70 °C to + 70 °C forL andK;}-70 °C to about –20 °C forG) and they, moreover, reflect the glassrubber transition of the binder.Poisson's ratio,, was found to decrease with increasing filler content and show a rise at the high temperature side of the experimentally accessible temperature range (about –20 °C) as a result of the approach of the glass-rubber transition.In addition to the velocities, the attenuation of both longitudinal and transverse waves was measured in the temperature ranges mentioned. It was found that in the hard region tan L as well as tan G are independent of the filler content within the accuracy of the measurements. In the rubbery region, however, tan L, increases with increasing filler content.Finally, the experimental data are compared with a simple macroscopic theory on the elastic properties of composite media.  相似文献   

10.
A generalized transverse wave is a propagating acceleration discontinuity on which the temperature and the entropy, together with their gradients, are continuous. In a heat-conducting elastic material the propagation and growth of such waves are uninfluenced by thermomechanical interaction. It is shown in this paper that in any given plane there is at least one direction in which a generalized transverse wave may propagate, and the existence is also proved of at least one direction in which a pair of generalized transverse waves may travel. Necessary and sufficient conditions are established for the speeds of propagation of these waves to be real. Relationships between transverse and generalized transverse waves are also studied, and in the last two sections of the paper the directions in which generalized transverse waves may propagate in an isotropic heat-conducting elastic material are systematically worked out and classified.  相似文献   

11.
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.  相似文献   

12.
L.R.F. Rose 《Wave Motion》1984,6(4):359-361
A relation is derived between the energy radiated by straight-crested Rayleigh waves and the amplitude of the vertical component of the displacement at the surface. This relation involves a constant of proportionality which depends in a complicated manner on Poisson's ratio, but a simple, quadratic, approximation is derived which is accurate to within 1%. The corresponding relation between the radiated energy and the amplitude of surface displacement for cylindrical surface waves is also derived and is used to show the influence of Poisson's ratio on the partition of energy between the body waves and the surface wave from two point sources.  相似文献   

13.
Summary The propagation of elastic waves (both longitudinal and transverse) through polyurethane rubbers filled with different amounts of sodium chloride particles was studied at 0.8 MHz and 5 MHz. At a constant filler concentration (∼10% by volume), the velocity of these waves appeared to be independent of filler size. On the other hand, both velocities were found to increase with filler content. From the wave velocities, the effective modulus for longitudinal waves, L, bulk modulus, K, and shear modulus, G, were calculated according to the relations for a homogeneous isotropic material. All three moduli appear to be monotonically increasing functions of filler content, c, over the whole experimentally accessible temperature range (−80°C to +80°C for L and K; −80°C to about −30°C for G) and they, moreover, reflect the glass-rubber transition of the binder. Poissons ratio, μ, was found to decrease with increasing filler content and shows a rise at about −30°C as a result of the approach of the glass-rubber transition. The attenuation of the elastic waves was also measured in the temperature ranges mentioned. For filler particles beyond a critical size both tan δL and tan δG in the hard region are independent of the filler content within the accuracy of the measurements. The critical size depends on the type of wave and on its frequency. In the rubbery region, however, tan δL increases with particle size (at a constant content of 10% by volume) and even shows an enhancement with the smallest particles (1–5 μ) at 0.8 MHz. Moreover, it is found that for the same filler size tan δL increases with filler content. In some cases an anomalous damping behaviour was found, such that in the rubbery region the attenuation rises indefinitely with temperature. For filler particles larger than the above-mentioned critical size, tan δG and tan δL increase in the hard region as well. Finally, the experimental results are compared with existing theories on the elastic properties of and wave propagation through composite media.  相似文献   

14.
15.
Travelling waves in an incompressible, infinitely conducting, inviscid fluid of variable density are investigated under the influence of a horizontal magnetic field and Coriolis force. Periodic solutions are found in the limit of infinite vertical wave length. Phase diagrams are drawn to show the solution.  相似文献   

16.
The effect of dust charge fluctuation on the existence and propagation of dust acoustic waves in unmagnetized dusty plasma is studied. Dispersion relation for the dust acoustic waves with temporal dust charge fluctuations is calculated based on the reductive perturbation technique. By considering two different limiting cases of the dust charging frequency, it is shown that the dusty plasma system gives rise to linear or nonlinear dust acoustic waves. The well-known collisionless damping of two existing normal modes and one purely damped mode are recovered when the dust charging frequency is comparable to the dust acoustic wave frequency. On the other hand, when the dust charging frequency is considerably higher than the wave frequency, it is then possible to derive a nonlinear Schrödinger type equation with envelope soliton as solution.  相似文献   

17.
18.
Expressions are obtained for the electromagnetic fields transmitted through a time-varying dielectric layer when a plane wave is incident normally upon one interface. Solutions are obtained for the case when the dielectric constant is changed in a stepwise fashion, and also for the case when the dielectric constant varies slowly and continuously. It is found that the inclusion of the boundary effects gives rise to frequency components in the transmitted signal which were not predicted by previous theories.Nomenclature c speed of light in vacuum - E electric field strength - H magnetic field strength - L thickness of the dielectric slab - n unit normal to the slab surface - r x–L - R reflection coefficient - t time - T transmission coefficient at x=0 - v speed of light in dielectric - x position - relative permittivity - transmission coefficient at x=L - 0 incident signal frequency (radians/sec) - instantaneous frequency (radians/sec)  相似文献   

19.
This is a continuation of a previous paper on the problem of plastic wave propagation in a semiinfinite bar subjected to an axially-applied impact stress. In the present paper the problem of unloading waves is considered. Malvern's strain-rate theory is applied and both the case of elastic unloading and the case of elasticviscoplastic unloading are considered. A theoretical relationship between the rate-independent and the ratedependent theories is established. A bilinear stress-strain curve is considered, valid for both loading, instantaneous unloading, and linear unloading. Both the elastic and elastic-viscoplastic unloading cases are considered and by using the method of characteristics and an IBM 7040-7094 digital computer it is shown that for the elasticviscoplastic case there exists a lower quasiplateau during unloading. This quasiplateau depends on the rate of unloading.  相似文献   

20.
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