共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
A. N. Ganzhelo 《Fluid Dynamics》2009,44(4):621-629
The problem of a system consisting of n+m shock waves which realizes the maximum dynamic pressure is solved for given Mach numbers ahead of the first and the closing
shocks provided that the sum of the flow turning angles in the last m waves is equal to the sum of the turning angles in the initial n waves minus the angle of attack. The corresponding necessary conditions of optimality of this shock-wave system, which constitutes
a system of nonlinear algebraic equations, are obtained. An efficient iteration method of solving this system of equations,
which makes it possible to solve the problem with high accuracy, is developed. The results of solving the problem make it
possible to select the optimum supersonic air intake configuration in the preliminary design stage and in the case of a large
number of shocks to estimate the limiting air intake parameters and the processes taking place in the air intake. 相似文献
3.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》2002,43(5):661-670
The paper studies simple waves of the shallowwater equations describing threedimensional wave motions of a rotational liquid in a freeboundary layer. Simple wave equations are derived for the general case. The existence of unsteady or steady simple waves adjacent continuously to a given steady shear flow along a characteristic surface is proved. Exact solutions of the equations describing steady simple waves were found. These solutions can be treated as extension of Prandtl–Mayer waves for sheared flows. For shearless flows, a general solution of the system of equations describing unsteady spatial simple waves was found. 相似文献
4.
A. N. Ganzhelo 《Fluid Dynamics》2012,47(2):254-262
The problem of a symmetric system consisting of 2n pairs of intersecting shock waves in a plane breaking duct which realizes the maximum total pressure is solved for given
Mach numbers upstream of the leading shocks and downstream of the closing shocks provided that in each pair consisting of
impinging and reflected waves the flow turning angles are equal in absolute values and have opposite directions. The corresponding
necessary conditions of optimality of this shock-wave system, which constitutes a system of nonlinear algebraic equations,
are obtained. An efficient iteration method of solving this system of equations, which makes it possible to solve the above-mentioned
problem with high accuracy, is developed. An approximate analytic solution is obtained for large n. The results of solving the problem make it possible to select the optimum configuration of the plane internal-compression
duct. 相似文献
5.
A. A. Chesnokov 《Journal of Applied Mechanics and Technical Physics》2001,42(4):628-637
A mathematical model for axisymmetric eddy motion of a perfect incompressible fluid in a long tube with thin elastic walls is proposed. Necessary and sufficient conditions for hyperbolicity of the system of equations of motion for flows with monotonic radial velocity profiles are formulated. The propagation velocities of the characteristics of the system under study and the characteristic shape of this system are calculated. The existence of simple waves continuously attached to a given steady shear flow is proved. The group of transformations admitted by the system is found, and submodels that determine invariant solutions are given. By integrating factorsystems, new classes of exact solutions of equations of motion are found. 相似文献
6.
Yu. V. Nemirovskii K. M. Shlemenzon 《Journal of Applied Mechanics and Technical Physics》1981,22(3):426-434
In the present work, the dynamic problem of coupled thermoelasticity with the most general type of nonuniformity and anisotropy is analyzed. The hyperbolic nature of the system of equations of coupled thermoelasticity is demonstrated, effects of extinction of separate waves by superposition of elastic and thermoelastic wave fronts are investigated, and the interrelationship of different orders of discontinuity of stresses, displacements, and temperature is determined. The case of the uncoupled problem of thermoelasticity is especially analyzed. Sufficient conditions are obtained for the dynamic density for wave processes in thermoelasticity, previously investigated for boundary value problems of hyperbolic systems of second order differential equations [1], andelastic stress waves [2] are obtained. The generally accepted system of tensor notation for the theory of thermoelasticity is used [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 154–163, May–June, 1981. 相似文献
7.
V. V. Levchenko 《International Applied Mechanics》2004,40(1):97-102
An exact solution is found for magnetoelastic shear waves in an infinite structure consisting of three metallized layers. The core layer is ferrite and the face layers are nonmagnetic dielectrics. The wave process in the layers is described by a linearized system of magnetoelastic equations. The problem posed is reduced to a system of linear algebraic equations. The existence conditions for an undamped solution to this system yield the existence conditions for magnetoelastic bulk waves. The dispersion relations derived are analyzed in detail 相似文献
8.
Two-dimensional stress waves in a general incompressible elastic solid are investigated. First, basic equations for simple waves and shock waves are presented for a general strain energy function. Then the characteristic wave speeds and the associated characteristic vectors are deduced. It is shown that there usually exist two simple waves and two shock waves. Finally, two examples are given for the case of plane strain deformation and antiplane strain deformation, respectively. It is proved that, in the case of plane strain deformation the oblique reflection problem of a plane shock is not solvable in general. 相似文献
9.
M. D. Kartalev 《Fluid Dynamics》1971,6(2):190-196
Stationary simple waves in a plasma with anisotropic pressure are investigated on the basis of the hydrodynamic equations of Chew, Goldberger, and Low. In Sec. 1, for the case where the vectors of the average flow velocity and the magnetic field intensity are parallel, the system of equations is reduced to two quasilinear equations for the velocity components. In Sec. 2 the equations for the characteristics are obtained, the system being assumed to be hyperbolic. For the special case of irrotational flow the character of simple waves in flows adjacent to various contours is studied. Section 3 contains a qualitative investigation of changes in the flow parameters in simple waves. In Sec. 4 the possibility of a transition to an unstable state of the plasma is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 12–19, March–April, 1971.The author thanks V. B. Baranov for the formulation of the problem and for his advice and constant attention to the work and also A. G. Kulikovskii for discussion of the results. 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.
L. A. Tkacheva 《Fluid Dynamics》2003,38(3):465-481
The problem of the behavior of a floating elastic strip-shaped plate in waves is considered. A new numerical method for solving this problem based on the Wiener-Hopf technique is proposed. The solution of the boundary value problem is reduced to an infinite system of linear algebraic equations which satisfies the reduction conditions. The calculation results are compared both with experiment and with the calculations of other authors. In the case of short incident waves the system of equations obtained can be essentially simplified. Three short-wave approximations are proposed, namely, the single-mode, four-mode and uniform approximations, which ensure good agreement with calculations based on the complete model. Simple explicit formulas are obtained for the single-mode and uniform approximations. 相似文献
12.
We consider the initial-value problem for a system of coupled Boussinesq equations on the infinite line for localised or sufficiently rapidly decaying initial data, generating sufficiently rapidly decaying right- and left-propagating waves. We study the dynamics of weakly nonlinear waves, and using asymptotic multiple-scale expansions and averaging with respect to the fast time, we obtain a hierarchy of asymptotically exact coupled and uncoupled Ostrovsky equations for unidirectional waves. We then construct a weakly nonlinear solution of the initial-value problem in terms of solutions of the derived Ostrovsky equations within the accuracy of the governing equations, and show that there are no secular terms. When coupling parameters are equal to zero, our results yield a weakly nonlinear solution of the initial-value problem for the Boussinesq equation in terms of solutions of the initial-value problems for two Korteweg-de Vries equations, integrable by the Inverse Scattering Transform. We also perform relevant numerical simulations of the original unapproximated system of Boussinesq equations to illustrate the difference in the behaviour of its solutions for different asymptotic regimes. 相似文献
13.
In this paper, we study strongly nonlinear axisymmetric waves in a circular cylindrical rod composed of a compressible Mooney-Rivlin material. To consider the travelling wave solutions for the governing partial differential system, we first reduce it to a nonlinear ordinary differential equation. By using the bifurcation theory of planar dynamical systems, we show that the reduced system has seven periodic annuluses with different boundaries which depend on four parameters. We further consider the bifurcation behavior of the phase portraits for the reduced one-parameter vector fields when other three parameters are fixed. Corresponding to seven different periodic annuluses, we obtain seven types of travelling wave solutions, including solitary waves of radial contraction, solitary waves of radial expansion, solitary shock waves of radial contraction, solitary shock waves of radial expansion, periodic waves and two types of periodic shock waves. These are physically acceptable solutions by the governing partial differential system. The rigorous parameter conditions for the existence of these waves are given. 相似文献
14.
T.J. Woodhead 《Wave Motion》1983,5(2):157-165
Ray theory is extended to consider the case of an accelerating disturbance which is producing waves in a rotating stratified fluid. Starting from the equations of motion, dispersion relations are derived for surface gravity waves, capillary waves, Rossby waves and internal-inertial waves. The wave system is studied in each case for the problem of a body starting impulsively from rest and for a body starting from rest and moving with constant acceleration. 相似文献
15.
V. E. Zakharov 《Journal of Applied Mechanics and Technical Physics》1968,9(2):190-194
We study the stability of steady nonlinear waves on the surface of an infinitely deep fluid [1, 2]. In section 1, the equations of hydrodynamics for an ideal fluid with a free surface are transformed to canonical variables: the shape of the surface (r, t) and the hydrodynamic potential (r, t) at the surface are expressed in terms of these variables. By introducing canonical variables, we can consider the problem of the stability of surface waves as part of the more general problem of nonlinear waves in media with dispersion [3,4]. The resuits of the rest of the paper are also easily applicable to the general case.In section 2, using a method similar to van der Pohl's method, we obtain simplified equations describing nonlinear waves in the small amplitude approximation. These equations are particularly simple if we assume that the wave packet is narrow. The equations have an exact solution which approximates a periodic wave of finite amplitude.In section 3 we investigate the instability of periodic waves of finite amplitude. Instabilities of two types are found. The first type of instability is destructive instability, similar to the destructive instability of waves in a plasma [5, 6], In this type of instability, a pair of waves is simultaneously excited, the sum of the frequencies of which is a multiple of the frequency of the original wave. The most rapid destructive instability occurs for capillary waves and the slowest for gravitational waves. The second type of instability is the negative-pressure type, which arises because of the dependence of the nonlinear wave velocity on the amplitude; this results in an unbounded increase in the percentage modulation of the wave. This type of instability occurs for nonlinear waves through any media in which the sign of the second derivative in the dispersion law with respect to the wave number (d2/dk2) is different from the sign of the frequency shift due to the nonlinearity.As announced by A. N. Litvak and V. I. Talanov [7], this type of instability was independently observed for nonlinear electromagnetic waves.The author wishes to thank L. V. Ovsyannikov and R. Z. Sagdeev for fruitful discussions. 相似文献
16.
In this paper we examine the resistance encountered by a system of normal stresses during its rectilinear motion along the surface of a viscous liquid of infinite depth. The problem is solved in the linear formulation, i.e., it is assumed that amplitudes of the waves which arise are small and the waves are shallow. The solution for the two-and three-dimensional problems is obtained in the general case in closed form. In the two-dimensional case a detailed study is made of the case when a constant pressure p0, moving with the constant velocity U, is given on a segment of length 2l. In the three-dimen-sional problem the case is studied when the normal stress is concentrated on a segment of a straight line of length 2l, which can replace a ship moving along a straight course with the constant velocity U. The integrals obtained in both cases are studied using the stationary phase method, the application of which for the three-dimensional integrals with respect to a volume with boundaries is justified in §1 of the paper. As a result we obtain equations for the wave resistance in the two- (§2) and three-dimensional (§3) cases. 相似文献
17.
A nonstationary problem is solved for a thin-walled piezoelectric transducer generating waves. The transducer is filled with a viscous and surrounded by a perfect compressible liquids. A method is developed to reduce this problem to a system of Volterra's integral equations. Calculations are performed to evaluate the effect of the viscous properties of the filler on the processes in the hydroelectroelastic system. 相似文献
18.
Abo-el-nour N. Abd-alla 《Mechanics Research Communications》1997,24(4):397
The present paper studies the dispersion relation of the radial vibrations of an orthotropic cylindrical tube. The effects of the magnetoelastic interaction on the problem are investigated. The problem is represented by the equations of elasticity taking into account the effect of the magnetic field as given by Maxwell's equations in the quasi-static approximation. The stress free conditions on the inner and outer surfaces of the hollow cylindrical cube are satisfied to form a dispersion relation in terms of the wavelength, the cylinder radii and the material constants. This study shows that waves in a solid body propagating under the influence of a superimposed magnetic field can differ significantly from those propagating in the absence of a magnetic field. The results have been verified numerically and represented graphically. 相似文献
19.
The method of multiple scales and the reductive perturbation method are reviewed and compared for calculating uniformly valid solutions of ion-acoustic waves. It is shown that they differ only in the choice of characteristic scales used in nondimensionalizing the problem. The inconsistent initial scaling used in the reductive method is later corrected by introducing artificially scaled variables to describe the solution in a form which remains uniformly valid in the far field. As a result this solution obeys the same evolution equations in both methods. Uncoupled nonlinear evolution equations describing waves traveling in opposite directions are derived using the multiple scale method for a number of different physical problems including the case of a general Galilean invariant system in conservation form. 相似文献
20.
A class of exact analytic solutions of the system of nonlinear long-wave equations is found. This class corresponds to the axisymmetric vibrations of an ideal incompressible homogeneous fluid in a rotating vessel in the shape of a paraboloid of revolution. The radial velocity of these motions is a linear function, and the azimuthal velocity and free surface displacements are polynomials in the radial coordinate with time-dependent coefficients. The nonlinear vibration frequency is equal to the frequency of the lowest mode of linear axisymmetric standing waves in the parabolic vessel. 相似文献