共查询到20条相似文献,搜索用时 31 毫秒
1.
M. A. Kulesh V. P. Matveenko M. V. Ulitin I. N. Shardakov 《Journal of Applied Mechanics and Technical Physics》2008,49(2):323-329
A study is made of waves in a Cosserat continuum, whose strain state is characterized by independent displacement and rotation
vectors. The propagation of longitudinal and transverse bulk waves is considered. Wave solutions are sought in the form of
wave trains specified by a Fourier spectrum of arbitrary shape. It is shown that if the solution is sought in the form of
three components of the displacement vector and three components of the rotation vector which depend on time and the longitudinal
coordinate, the initial system is split into two systems, one of which describes longitudinal waves, and the other transverse
waves. For waves of both types, dispersion relations and analytical solutions in displacement are obtained. The dispersion
characteristics of the solutions obtained differ from the dispersion characteristics of the corresponding classical elastic
solutions.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 196–203, March–April, 2008. 相似文献
2.
《Wave Motion》1986,8(5):415-438
From the equations of hydrodynamics and electrodynamics, a system of coupled nonlinear equations governing the propagation of plane electromagnetic waves in a collisionless electron plasma is obtained. It is shown that solitary wave solutions exists for both the longitudinal and transverse components of the electromagnetic field. It is found that the velocity of the electromagnetic vector solitary wave depends on the amplitudes of all components of the field linearly. The relations among the longitudinal and transverse components that support the solitary waves are determined for different values of plasma temperature. It is shown that while transverse solitary waves cannot exist, except when they are supported by longitudinal waves, the latter can exist by themselves. The interaction of the longitudinal solitary waves with each other is studied and an upper bound on the amplitudes of these waves is obtained. A Lagrangian density function and two conservation laws for the longitudinal wave equation are found. Frequency spectra of the solitary waves are calculated and their low frequency content is emphasized. 相似文献
3.
The scattering problem of a Lamb wave incident on a symmetric pair of surface-breaking transverse cracks in a plate is considered. The Lamb wave is assumed to be obliquely incident on the crack plane. Since the cracks are part-through, the scattered field will contain reflected as well as transmitted waves. The energy of the incoming wave is partitioned into reflected and transmitted wave modes. Energy coefficients of the reflected and transmitted waves are calculated as a function of incident frequency and crack depth. The incidence angle of the incoming wave is also treated as a parameter. Both the reflected and transmitted wave fields are considered as linear superpositions of all real and complex wave modes in the plate. Decomposition of modes is achieved with the help of an orthogonality condition based on the principle of reciprocal work. Continuity of displacement and stress fields is imposed at the crack plane. Energy coefficients for reflection and transmission are obtained from the mode amplitudes. Energy coefficients are shown to be a strong function of incident frequency and crack depth. Experiments are conducted with a PZT transducer network interacting with a symmetric pair of machined cracks in an aluminum plate. Trends predicted by the analysis are reflected in the experimental results. 相似文献
4.
5.
Yu. A. Drozdova 《Fluid Dynamics》2000,35(4):591-598
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
6.
A. Mahalov M. Moustaoui B. Nicolaenko K. L. Tse 《Theoretical and Computational Fluid Dynamics》2007,21(6):399-422
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.
《International Journal of Solids and Structures》2002,39(7):1777-1790
Based on the theories of anisotropic elasticity, piezoelectricity and elastic waves in solids, the propagation of antisymmetric Lamb waves in a biasing electric field is investigated in this paper. By solving the coupled differential equations of motion under a biasing electric field, the phase velocity equations of antisymmetric Lamb wave modes for electrically open and shorted cases are obtained, respectively. The beating effect arising from the difference between the phase velocity of the zero-order symmetric mode and antisymmetric mode exists in the plate when the plate has a thickness comparable to or slightly larger than the wavelength. The influence of the biasing electric field on the phase velocity, beat wavelength, mechanical displacement and stress fields for the lowest two antisymmetric modes of Lamb waves are discussed in detail. From the calculated results, it is seen that the phase velocity of the fundamental antisymmetric mode is especially sensitive to the applied biasing electric field. 相似文献
8.
《International Journal of Solids and Structures》2002,39(7):2031-2049
This paper is concerned with the effect of a biasing electric field on the propagation of Lamb waves in a piezoelectric plate. On the basis of three dimensional linear elastic equations and piezoelectric constitutive relations, the differential equations of motion under a biasing electric field are obtained and solved. Due to the symmetry of the plate, there are symmetric and antisymmetric modes with respect to the median plane of the piezoelectric plate. According to the characteristics of symmetric modes (odd potential state) and antisymmetric modes (even potential state), the phase velocity equations of symmetric and antisymmetric modes of Lamb wave propagation are obtained for both electrically open and shorted cases. The effect of a biasing electric field on the phase velocity, electromechanical coupling coefficient, stress field and mechanical displacement of symmetric and antisymmetric Lamb wave modes are discussed in this paper and an accompanying paper respectively. It is shown that the biasing electric field has significant effect on the phase velocity and electromechanical coupling coefficient, the time delay owning to the velocity change is useful for high voltage measurement and temperature compensation, the increase in the electromechanical coupling coefficient can be used to improve the efficiency of transduction. 相似文献
9.
10.
We study the vanishing viscosity limit of the compressible Navier–Stokes equations to the Riemann solution of the Euler equations
that consists of the superposition of a shock wave and a rarefaction wave. In particular, it is shown that there exists a
family of smooth solutions to the compressible Navier–Stokes equations that converges to the Riemann solution away from the
initial and shock layers at a rate in terms of the viscosity and the heat conductivity coefficients. This gives the first
mathematical justification of this limit for the Navier–Stokes equations to the Riemann solution that contains these two typical
nonlinear hyperbolic waves. 相似文献
11.
This paper deals with the linear stability of a liquid film flowing down an inclined plane. The Navier-Stokes equations were reduced into four evolution equations that describe the development of the film depth, the flow rate, the free surface velocity, and the wall shear stress, using the Karman-Polhausen boundary layer integral method. Thus, we were able to determine the stability threshold and approach well the critical wave number for long waves. The obtained results were found to be in good agreement with the experiments of Liu et al. 相似文献
12.
N. I. Ostrosablin 《Journal of Applied Mechanics and Technical Physics》2003,44(2):271-278
The simplest form of the matrix of elasticity moduli of an anisotropic material conducting purely longitudinal and transverse waves with an arbitrary direction of the wave normal is obtained. A generic solution of equations in displacements is represented in terms of three functions satisfying independent wave equations. In the case of planar deformation, this solution yields a complex representation coinciding with the Kolosov–Muskhelishvili formulas for an isotropic material. The formulas in the present work also determine an anisotropic material with Young's modulus identical for all directions, as in an isotropic medium. 相似文献
13.
基于线性三维弹性理论,采用勒让德正交多项式展开法,推导了波沿正交各向异性材料非主轴方向传播时的Lamb波耦合波动方程,并对耦合波动方程进行了数值求解.为验证该方法的适用性和正确性,首先将此方法应用于各向同性材料,并与已知的数据结果进行了比较;然后以单向纤维增强复合材料为例,计算了耦合Lamb波沿不同的非主轴方向传播时的相速度频散曲线,并分别研究了传播方向改变时低阶模态Lamb波和高阶模态Lamb波频散特性的变化.最后,针对潜在用于各向异性复合材料结构健康监测的耦合Lamb波低阶模态,给出了其在不同传播方向时的相速度分布和群速度分布.同时,结合低阶模态Lamb波的位移分布特性和材料的各向异性特点,阐释了S0模态对波的传播方向变化最为敏感的原因. 相似文献
14.
15.
《International Journal of Solids and Structures》2003,40(11):2645-2658
Wave scattering analysis implemented by boundary element methods (BEM) and the normal mode expansion technique is used to study the sizing potential of two-dimensional shaped defects in a wave guide. Surface breaking half-elliptical shaped defects of three opening lengths (0.3, 6.35 and 12.7 mm) and through-wall depths of 10–90% on a 10 mm thick steel plate were considered. The reflection and transmission coefficients of both Lamb and shear horizontal (SH) waves over a frequency range 0.05–2 MHz were studied. A powerfully practical result was obtained whereby the numerical results for the S0 mode Lamb wave and n0 mode SH wave at low frequencies showed a monotonic increase in signal amplitude with an increase in the defect through-wall depth. At high frequency (usually above the cut-off frequency of the A1 mode for Lamb waves and the n1 mode for SH waves, respectively), the monotonic trend does not hold in general due to the energy redistribution to the higher order wave modes. Guided waves impinging onto an internal stringer-like an inclusion were also studied. Both the Lamb and SH waves were shown to be insensitive to the stringer internal inclusions at low frequency. Experiments with piezoelectric Lamb wave transducers and non-contact SH wave electro-magnetic acoustic transducers (EMAT) verified some of the theoretical results. 相似文献
16.
A. Babin A. Mahalov B. Nicolaenko 《Theoretical and Computational Fluid Dynamics》1998,11(3-4):215-235
Three-dimensional nonhydrostatic Euler–Boussinesq equations are studied for Bu=O(1) flows as well as in the asymptotic regime of strong stratification and weak rotation. Reduced prognostic equations for
ageostrophic components (divergent velocity potential and geostrophic departure/thermal wind imbalance) are analyzed. We describe
classes of nonlinear anisotropic ageostrophic baroclinic waves which are generated by the strong nonlinear interactions between
the quasi-geostrophic modes and inertio-gravity waves. In the asymptotic regime of strong stratification and weak rotation
we show how switching on weak rotation triggers frontogenesis. The mechanism of the front formation is contraction in the
horizontal dimension balanced by vertical shearing through coupling of large horizontal and small vertical scales by weak
rotation. Vertical slanting of these fronts is proportional to μ−1/2 where μ is the ratio of the Coriolis and Brunt–V?is?l? parameters. These fronts select slow baroclinic waves through nonlinear
adjustment of the horizontal scale to the vertical scale by weak rotation, and are the envelope of inertio-gravity waves.
Mathematically, this is generated by asymptotic hyperbolic systems describing the strong nonlinear interactions between waves
and potential vorticity dynamics. This frontogenesis yields vertical “gluing” of pancake dynamics, in contrast to the independent
dynamics of horizontal layers in strongly stratified turbulence without rotation.
Received 8 April 1997 and accepted 29 March 1998 相似文献
17.
The paper discusses the results of theoretical and numerical analysis of the interaction of nonlinear elastic plane harmonic
waves in a composite material whose nonlinear properties are described by modeling it with a two-phase mixture. The interaction
of two transverse vertically polarized harmonic waves is studied using the method of slowly varying amplitudes. The truncated
and evolutionary equations as well as the Manley-Rowe relations are derived. The mechanism of energy pumping from a strong
pumping wave with frequency ω to a weak signal wave with frequency 3ω is analyzed. The switching mechanism for hypersonic
waves in a nonlinear elastic composite is similar to the switching mechanism observed in transistors
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 35–46, July 2007. 相似文献
18.
The paper presents theoretical results on the interaction of cubically nonlinear harmonic elastic plane waves in a nonlinear
material described by the Murnaghan potential. The interaction of two harmonic transverse waves is studied using the method
of slowly varying amplitude. Reduced and evolution equations and the Manley-Rowe relations are derived. An analysis is made
of the mechanism of energy transfer from the strong pumping wave, which has frequency ω, to the weak signal wave, which has
frequency 3ω because of this interaction. A switching mechanism for hypersonic waves in a nonlinear elastic material is described,
which is similar to the switching mechanism observed in transistors
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 61–70, June 2006. 相似文献
19.
L. P. Khoroshun 《International Applied Mechanics》1999,35(9):878-888
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
20.
A. V. Plekhanov 《International Applied Mechanics》1999,35(11):1117-1122
The equations of the iteration theory of nonshallow transversally isotropic laminated shells, which account for all the components
of the stress-strain state (SSS) and describe the inner SSS, potential, and vortex boundary effects, are obtained. The equations
are based on the method of expansion of SSS into series in transverse coordinate and the method of variation with respect
to the state being determined. The order of the equations does not depend on the number of layers and expansion terms that
approximate the displacement and stress. The accuracy of the solution for the inner SSS and boundary effects is estimated.
Pridneprovskaya State Academy of Building and Architecture, Dnepropetrovsk, Ukraine. Translated from Prikladnaya Mekhanika,
Vol. 35, No. 11, pp. 40–45, November, 1999. 相似文献