共查询到20条相似文献,搜索用时 15 毫秒
1.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》2007,48(3):303-309
The classical shallow-water equations describing the propagation of long waves in flow without a shear of the horizontal velocity
along the vertical coincide with the equations describing the isentropic motion of a polytropic gas for a polytropic exponent
γ = 2 (in the theory of fluid wave motion, this fact is called the gas-dynamic analogy). A new mathematical model of long-wave
theory is derived that describes shear free-boundary fluid flows. It is shown that in the case of one-dimensional motion,
the equations of the new model coincide with the equations describing nonisentropic gas motion with a special choice of the
equation of state, and in the multidimensional case, the new system of long-wave equations differs significantly from the
gas motion model. In the general case, it is established that the system of equations derived is a hyperbolic system. The
velocities of propagation of wave perturbations are found.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 8–15, May–June, 2007. 相似文献
2.
Constructing an analytical solution for lamb waves using the cosserat continuum approach 总被引:2,自引:0,他引:2
M. A. Kulseh V. P. Matveenko I. N. Shardakov 《Journal of Applied Mechanics and Technical Physics》2007,48(1):119-125
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.
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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
3.
An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic
porous medium containing two immiscible fluids. The theory is based on the Berryman–Thigpen–Chin (BTC) model, in which capillary
pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently
low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the time domain.
These partial differential equations describe two independent modes of dilatational wave motion that are analogous to the
Biot fast and slow compressional waves in a single-fluid system. The equations can be solved analytically under a variety
of initial and boundary conditions. The stipulation of “low frequency” underlying the derivation of our equations in the time
domain is shown to require that the excitation frequency of wave motions be much smaller than a critical frequency. This frequency
is shown to be the inverse of an intrinsic time scale that depends on an effective kinematic shear viscosity of the interstitial
fluids and the intrinsic permeability of the porous medium. Numerical calculations indicate that the critical frequency in
both unconsolidated and consolidated materials containing water and a nonaqueous phase liquid ranges typically from kHz to
MHz. Thus engineering problems involving the dynamic response of an unsaturated porous medium to low excitation frequencies
(e.g., seismic wave stimulation) should be accurately modeled by our equations after suitable initial and boundary conditions
are imposed. 相似文献
4.
5.
We study a model for the lateral propagation of a combustion front through a porous medium with two parallel layers having different properties. The reaction involves oxygen and a solid fuel. In each layer, the model consists of a nonlinear reaction–diffusion–convection system, derived from balance equations and Darcy’s law. Under an incompressibility assumption, we obtain a simple model whose variables are temperature and unburned fuel concentration in each layer. The model includes heat transfer between the layers. We find a family of traveling wave solutions, depending on the heat transfer coefficient and other system parameters, that connect a burned state behind the combustion front to an unburned state ahead of it. These traveling waves are strong: they correspond to connecting orbits of a system of five ordinary differential equations that lie in the unstable manifold of a hyperbolic saddle and the stable manifold of a nonhyperbolic equilibrium. We argue that for physically relevant initial conditions, traveling waves that correspond to connecting orbits that approach the nonhyperbolic equilibrium along its center direction do not occur. When the heat transfer coefficient is small, we prove that strong traveling waves exist for a small range of system parameters, near parameter values where the two layers individually admit strong traveling waves with the same speed. When the heat transfer coefficient is large, we prove that strong traveling waves exist for a very large range of parameters. For small heat transfer, combustion typically does not occur simultaneously in the two layers; for large heat transfer, it does. The proofs use geometric singular perturbation theory. We give a numerical method to solve the nonlinear problem, and we present numerical simulations that indicate that the traveling waves we have found are in fact the dominant feature of solutions. 相似文献
6.
G. L. Komissarova 《International Applied Mechanics》2007,43(9):988-999
The properties of harmonic surface waves in an elastic cylinder made of a rigid material and filled with a fluid are studied.
The problem is solved using the dynamic equations of elasticity and the equations of motion of a perfect compressible fluid.
It is shown that two surface (Stoneley and Rayleigh) waves exist in this waveguide system. The first normal wave generates
a Stoneley wave on the inner surface of the cylinder. If the material is rigid, no normal wave exists to transform into a
Rayleigh wave. The Rayleigh wave on the outer surface forms on certain sections of different dispersion curves. The kinematic
and energy characteristics of surface waves are analyzed. As the wave number increases, the phase velocities of all normal
waves, except the first one, tend to the sonic velocity in the fluid from above
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 48–62, September 2007. 相似文献
7.
An approximate solution of an initial-boundary-value problem appropriate for the semiaxist>0 (t is time) is constructed for a system of integrodifferential equations which describes the waves excited in an initially stationary
unbounded heavy two-layer fluid by a vertically oscillating sphere located at a distance from the interface that is significantly
greater than its radius. The shape of the steady-state wave is found by passing to the limit as time increases indefinitely.
The wave resistance experienced by the sphere during the transient process and in the steady-state regime is studied as a
function of frequency.
Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–133, March–April,
1998. 相似文献
8.
V. V. Ostapenko 《Journal of Applied Mechanics and Technical Physics》1999,40(4):647-654
A mathematical model is developed for formation and propagation of discontinuous waves caused by sliding of a shoreside landslide
into water. The model is based on the equations of a two-layer “shallow liquid” with specially introduced “dry friction” in
the low layer, which allows one to describe the joint motion of the landslide and water. An explicit difference scheme approximating
these equations is constructed, and it is used to develop a numerical algorithm for simulating the motion of the free boundaries
of both the landslide and water (in particular, the propagation of a water wave along a dry channel, incidence of the wave
on the lakeside, and flow over obstacles).
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 109–117, July–August, 1999. 相似文献
9.
V. I. Bukreev 《Journal of Applied Mechanics and Technical Physics》1999,40(3):399-406
Experimental data on surface solitary waves generated by five methods are given. These data and literature information show
that at amplitudes 0.2<a/h<0.6 (h is the initial depth of the liquid), experimental solitary waves are in good agreement with
their theoretical analogs obtained using the complete model of liquid potential flow. Some discrepancy is observed in the
range of small amplitudes. The reasons why free solitary waves of theoretically limiting amplitude have not been realized
in experiments are discussed, and an example of a forced wave of nearly limiting amplitude is given. The previously established
fact that during evolution from the state of rest, undular waves break when the propagation speed of their leading front reaches
the limiting speed of propagation of a solitary wave is confirmed.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 44–52, May–June, 1999. 相似文献
10.
We consider the question of stability for planar wave solutions that arise in multidimensional conservation laws with only
fourth-order regularization. Such equations arise, for example, in the study of thin films, for which planar waves correspond
to fluid coating a pre-wetted surface. An interesting feature of these equations is that both compressive, and undercompressive,
planar waves arise as solutions (compressive or undercompressive with respect to asymptotic behavior relative to the un-regularized
hyperbolic system), and numerical investigation by Bertozzi, Münch, and Shearer indicates that undercompressive waves can
be nonlinearly stable. Proceeding with pointwise estimates on the Green's function for the linear fourth-order convection–regularization
equation that arises upon linearization of the conservation law about the planar wave solution, we establish that under general
spectral conditions, such as appear to hold for shock fronts arising in our motivating thin films equations, compressive waves
are stable for all dimensions d≧2 and undercompressive waves are stable for dimensions d≧3. (In the special case d=1, compressive waves are stable under a very general spectral condition.) We also consider an alternative spectral criterion
(valid, for example, in the case of constant-coefficient regularization), for which we can establish nonlinear stability for
compressive waves in dimensions d≧3 and undercompressive waves in dimensions d≧5. The case of stability for undercompressive waves in the thin films equations for the critical dimensions d=1 and d=2 remains an interesting open problem. 相似文献
11.
Shallow water waves and a host of long wave phenomena are commonly investigated by various models of nonlinear evolution equations.
Examples include the Korteweg–de Vries, the Camassa–Holm, and the Whitham–Broer–Kaup (WBK) equations. Here a generalized WBK
system is studied via the multi-linear variable separation approach. A special class of wave profiles with discontinuous derivatives
(“peakons”) is developed. Peakons of various features, e.g. periodic, pulsating or fractal, are investigated and interactions
of such entities are studied.
The project supported by the National Natural Science Foundation of China (10475055, 10547124 and 90503006), and the Hong
Kong Research Grant Council Contract HKU 7123/05E. 相似文献
12.
A comparative analysis of two types of hyperelastic waves—plane waves (with plane front) and cylindrical waves (with curved
front)—is offered. The propagation of the waves is studied theoretically for quadratically nonlinear hyperelastic media and
numerically for a class of unidirectional fibrous composite materials. Hyperelasticity is described using the classical Murnaghan
potential and a structural model of the first order—the model of effective constants. The internal structure of materials
is described by this model and is at the micro-or nanolevels in numerical analysis. Particular attention is given to the evolution
of the wave profile. It is studied in three stages: (i) derivation of nonlinear wave equations, (ii) construction of solutions
in the form of plane and cylindrical waves, and (iii) numerical analysis of the evolution of these waves in composites with
microlevel (Thornel) or nanolevel (Z-CNT) fibers. The main similarities and differences between plane longitudinal and cylindrical
waves are shown. The most unexpected result is the striking difference between the evolution patterns numerically observed
for plane and cylindrical wave profiles
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 21–46, October 2006. 相似文献
13.
V. V. Mykhas’kiv N. D. Grilitskii I. O. Butrak 《Journal of Applied Mechanics and Technical Physics》2006,47(4):556-563
A three-dimensional wave field formed owing to diffraction of low-frequency waves on a curved crack in an infinite elastic
solid at a large distance from the defect is studied by the method of boundary integral equations. Direction diagrams of the
scattered field versus the excentricity of the crack surface and wavenumber are obtained for different directions of incidence
of planar longitudinal waves onto a gently sloping spheroidal crack.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 115–123, July–August, 2006. 相似文献
14.
A procedure of deriving nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical
waves in composite materials modeled by a mixture with two elastic constituents is outlined. Nonlinearity is introduced by
metric coefficients, Cauchy-Green strain tensor, and Murnaghan potential. It is the quadratic nonlinearity of all governing
relations. For a configuration (state) dependent on the radial coordinate and independent of the angular and axial coordinates,
quadratically nonlinear wave equations for stresses are derived and a relationship between the components of the stress tensor
and partial strain gradient is established. Four combinations of physical and geometrical nonlinearities in systems of wave
equations are examined. Nonlinear wave equations are explicitly written for three of the combinations
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 63–72, June 2007. 相似文献
15.
T. J. T. Spanos 《Transport in Porous Media》2009,79(1):135-148
It has been known since the time of Biot–Gassman theory (Biot, J Acoust Soc Am 28:168–178, 1956, Gassmann, Naturf Ges Zurich
96:1–24, 1951) that additional seismic waves are predicted by a multicomponent theory. It is shown in this article that if
the second or third phase is also an elastic medium then multiple p and s waves are predicted. Futhermore, since viscous dissipation
no longer appears as an attenuation mechanism and the media are perfectly elastic, these waves propagate without attenuation.
As well, these additional elastic waves contain information about the coupling of the elastic solids at the pore scale. Attempts
to model such a medium as a single elastic solid causes this additional information to be misinterpreted. In the limit as
the shear modulus of one of the solids tends to zero, it is shown that the equations of motion become identical to the equations
of motion for a fluid filled porous medium when the viscosity of the fluid becomes zero. In this limit, an additional dilatational
wave is predicted, which moves the fluid though the porous matrix much similar to a heart pumping blood through a body. This
allows for a connection with studies which have been done on fluid-filled porous media (Spanos, 2002). 相似文献
16.
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.
G. L. Komissarova 《International Applied Mechanics》2008,44(4):419-430
The properties of harmonic surface waves in a fluid-filled cylinder made of a compliant material are studied. The wave motions
are described by a complete system of dynamic equations of elasticity and the equation of motion of a perfect compressible
fluid. An asymptotic analysis of the dispersion equation for large wave numbers and a qualitative analysis of the dispersion
spectrum show that there are two surface waves in this waveguide system. The first normal wave forms a Stoneley wave on the
inside surface with increase in the wave number. The second normal wave forms a Rayleigh wave on the outside surface. The
phase velocities of all the other waves tend to the velocity of the shear wave in the cylinder material. The dispersion, kinematic,
and energy characteristics of surface waves are analyzed. It is established how the wave localization processes differ in
hard and compliant materials of the cylinder
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 72–86, April 2008. 相似文献
19.
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
20.
V. M. Shul'ga 《International Applied Mechanics》1999,35(4):356-365
A general case of propagation of acoustoelectric waves of nonaxial direction is studied. The basis system of equations of
the wave problem in circular cylindrical coordinates is reduced to eight Hamiltonian equations in the radial component. For
harmonic waves, the generalized spectral problem is solved by numerical methods. Particular cases of the general problem are
considered. The results of solution of concrete problems are analyzed.
Taras Shevchenko University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 37–46, April, 1999. 相似文献