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1.
The problem of propagation of a Lamb elastic wave in a thin plate is considered using the Cosserat continuum model. The deformed state is characterized by independent displacement and rotation vectors. Solutions of the equations of motion are sought in the form of wave packets specified by a Fourier spectrum of an arbitrary shape for three components of the displacement vector and three components of the rotation vector which depend on time, depth, and the longitudinal coordinate. The initial system of equations is split into two systems, one of which describes a Lamb wave and the second corresponds to a transverse wave whose amplitude depends on depth. Analytical solutions in displacements are obtained for the waves of both types. Unlike the solution for Lamb waves, the solution obtained for the transverse wave has no analogs in classical elasticity theory. The solution for the transverse wave is compared with the solution for the Lamb wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 143–150, January–February, 2007. An erratum to this article is available at .  相似文献   

2.
This article deals with a certain type of wave in an infinite elastic medium. In contrast to ordinary longitudinal and transverse waves, the amplitude of the type of wave in question depends sinusoidally on the coordinates of a plane which is transverse to the direction of propagation of the wave, i.e., the wave is actually a packet of travelling and stationary waves. Longitudinal waves of this type are always coupled with transverse waves, while transverse waves of the given type may be coupled with longitudinal waves or another transverse wave or may exist as a single wave in the form of a packet containing a travelling wave and a stationary wave. The coupled waves have two phase velocities, which depend on the mechanical properties of the medium, the frequency of vibration, and the wave numbers of the stationary waves. Coupled surface waves in an elastic medium are more general in character than Rayleigh waves; they exhibit dispersion, and they can be used to explain certain seismological observations made during earthquakes—the complete absence of vertical displacements in some cases and the frequent occurrence of horizontal displacements parallel to the wave front. Allowing for the coupling of elastic waves in a layer leads to a more general characteristic equation than the equation obtained in the Rayleigh-Lamb problem. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 19–28, September, 1999.  相似文献   

3.
A problem of propagation of longitudinal and transverse waves in a multimodulus elastic isotropic medium is considered. In the model used, the medium is described by a potential depending on three invariants of strains, which allows the influence of preliminary deformation of the medium on the longitudinal and transverse velocities to be taken into account. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 176–182, July–August, 2009.  相似文献   

4.
The velocity and the rate of decay of a strain wave in a layer of a viscoelastic material rigidly fixed on a solid foundation are determined. The wave structure (ratio of the longitudinal to the transverse displacement) and the profiles of these displacements are analyzed. Attenuation of waves in the first mode is found to be more significant than that in an infinite space. The most intense decay is observed at resonance frequencies. A strong effect of compressibility of the medium on wave parameters is revealed. Conditions at which such a system operates as a waveguide are found. For a loss tangent higher than 0.13 (for an incompressible medium), the character of the dispersion dependence is observed to change drastically: the wave velocity decreases with decreasing frequency. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 104–111, May–June, 2006.  相似文献   

5.
The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasi-thermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.  相似文献   

6.
The generation and physical characteristics of inertia-gravity waves radiated from an unstable forced jet at the tropopause are investigated through high-resolution numerical simulations of the three-dimensional Navier–Stokes anelastic equations. Such waves are induced by Kelvin–Helmholtz instabilities on the flanks of the inhomogeneously stratified jet. From the evolution of the averaged momentum flux above the jet, it is found that gravity waves are continuously radiated after the shear-stratified flow reaches a quasi-equilibrium state. The time–vertical coordinate cross-sections of potential temperature show phase patterns indicating upward energy propagation. The sign of the momentum flux above and below the jet further confirms this, indicating that the group velocity of the generated waves is pointing away from the jet core region. Space–time spectral analysis at the upper flank level of the jet shows a broad spectral band, with different phase speeds. The spectra obtained in the stratosphere above the jet show a shift toward lower frequencies and larger spatial scales compared to the spectra found in the jet region. The three-dimensional character of the generated waves is confirmed by analysis of the co-spectra of the spanwise and vertical velocities. Imposing the background rotation modifies the polarization relation between the horizontal wind components. This out-of-phase relation is evidenced by the hodograph of the horizontal wind vector, further confirming the upward energy propagation. The background rotation also causes the co-spectra of the waves high above the jet core to be asymmetric in the spanwise modes, with contributions from modes with negative wavenumbers dominating the co-spectra. Dedicated to the memory of our colleague Dr. Binson Joseph  相似文献   

7.
For the coupled model of a thermoviscoelastic rod of equilateral triangular cross section, two exact solutions are obtained for the cases where a normal displacement and a shear stress or a tangential displacement and a normal stress are specified on the lateral surface of the rod. A dimensionless parameter R0 is introduced to judge the appropriateness of taking into account the coupling in the formulation of the problem. Formulas are given for the velocities and lengths of the temperature, shear, and longitudinal waves, which can be used in experiments to determine the physical properties of thermoviscoelastic materials. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 128–143, July–August, 2007.  相似文献   

8.
Nonlinear waves of small amplitude in wide horizontal channels are considered. The channel depth is assumed to be a function weakly dependent on the transverse coordinate. To describe the waves, the two-dimensional Boussinesq equations in the form obtained in this paper are used. Stationary solutions in the form of a soliton followed by a set of sinusoidal waves are found. The phase velocity of these waves in the channel direction is equal to the soliton velocity. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 147–155, July–August, 2000. The work was financially supported by the Russian Foundation for Basic Research (project No. 99-01-00277).  相似文献   

9.
Free vibrations of layered conical shell frusta of differently varying thickness are studied using the spline function approximation technique. The equations of motion for layered conical shells, in the longitudinal, circumferential and transverse displacement components, are derived using extension of Love’s first approximation theory. Assuming the displacement components in a separable form, a system of coupled equations on three displacement functions are obtained. Since no closed form solutions are generally possible, a numerical solution procedure is adopted in which the displacement functions are approximated by cubic and quintic splines. A generalized eigenvalue problem is obtained which is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibrations of two-layered conical shells, made up of several types of layer materials and supported differently at the ends are considered. Linear, sinusoidal and exponential variations in thickness of layers are assumed. Parametric studies are made on the variation of frequency parameter with respect to the relative layer thickness, cone angle, length ratio, type of thickness variation and thickness variation parameter. The effect of neglecting the coupling between bending and stretching is also analysed.  相似文献   

10.
It is shown that, in the planar case, the system of constitutive equations of the linear elasticity theory should contain five independent equations. In the classical theory, only three equations are formulated, while the other two are contained in implicit form in the postulate of diffeomorphism, which is the assumption of smoothness of the displacement field. A closed elasticity model is constructed without the assumption of diffeomorphism, and it contains a structural parameter having a dimension of length. It is shown that, in a static version, macrodeformations depend on stresses and second derivatives of stresses with respect to the coordinates, while there is dispersion of longitudinal and transverse waves in the dynamics.  相似文献   

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