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1.
A. A. Chesnokov 《Journal of Applied Mechanics and Technical Physics》1999,40(3):420-430
A mathematical model of the vortex motion of an ideal two-layer fluid in a narrow straight channel is considered. The fluid
motion in the Eulerian-Lagrangian coordinate system is described by quasilinear integrodifferential equations. Transformations
of a set of the equations of motion which make it possible to apply the general method of studying integrodifferential equations
of shallow-water theory, which is based on the generalization of the concepts of characteristics and the hyperbolicity for
systems with operator functionals, are found. A characteristic equation is derived and analyzed. The necessary hyperbolicity
conditions for a set of equations of motion of flows with a monotone-in-depth velocity profile are formulated. It is shown
that the problem of sufficient hyperbolicity conditions is equivalent to the solution of a certain singular integral equation.
In addition, the case of a strong jump in density (a heavy fluid in the lower layer and a quite lightweight fluid in the upper
layer) is considered. A modeling that results in simplification of the system of equations of motion with its physical meaning
preserved is carried out. For this system, the necessary and sufficient hyperbolicity conditions are given.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40,
No. 3, pp. 68–80, May–June, 1999. 相似文献
2.
A. A. Chesnokov 《Journal of Applied Mechanics and Technical Physics》2000,41(4):593-603
We obtain new classes of invariant solutions of the integrodifferential equations describing the propagation of nonlinear
concentration waves in a rarefied bubbly fluid. For all the solutions obtained, trajectories of particle motion in phase space
are calculated. The stability of some flows is studied in a linear approximation. In several cases, the construction of solutions
reduces to an integrodifferential equation of the second kind, which can be solved by the iteration method.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41,
No. 4, pp. 21–32, July–August, 2000. 相似文献
3.
V. D. Bondar' 《Journal of Applied Mechanics and Technical Physics》2000,41(3):547-555
The averaged rotations and other mechanical parameters at finite plane strains of an elastic material, which are characterized
by a linear relation between the Cauchy stresses and the Almansi strains, are studied. The form of the elastic potential is
determined. The displacement problem is reduced to a boundary-value problem for complex potentials, which is solved in terms
of Cauchy-type integrals for the specified boundarys displacements. The results obtained are compared with the linear solution.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41,
No. 3, pp. 187–196, May–June, 2000. 相似文献
4.
L. V. Ovsyannikov 《Journal of Applied Mechanics and Technical Physics》1999,40(2):191-197
The notion of a “simple” solution of a system of differential equations that admit a local Lie group G of transformations
of the basic space is considered as an invariant H-solution of type (0, 0) with respect to the subgroup HυG. Such solutions
are attractive since they are described by explicit formulas that provide a clear physical interpretation for them. For gas-dynamic
equations with a polytropic gas law, all simple solutions that are not related to special forms of gas flow are listed. Examples
of simple solutions are given and the collapse phenomenon, which has been previously studied for barochronic flows, is described.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 5–12, March–April, 1999. 相似文献
5.
B. A. Lugovtsov 《Journal of Applied Mechanics and Technical Physics》2000,41(5):870-878
The stability of steady axisymmetricMHD flows of an inviscid, incompressible, perfectly conducting fluid with respect to swirling—perturbations of the azimuthal
components of the velocity field—is studied in a linear approximation. It is shown that for flows similar to a magnetohydrodynamic
Hill-Shafranov vortex, the problem reduces to a one-dimensional problem on a closed streamline of the unperturbed flow (the
arc length of the streamline is the spatial coordinate). A spectral boundary-value eigenvalue problem is formulated for a
system of two ordinary differential equations with periodic coefficients and periodic boundary conditions. Sufficient conditions
under which swirling is impossible are obtained. Numerical solution of the characteristic equation shows that, under certain
conditions, for each streamline there is a real eigenvalue that yields monotonic exponential growth of the initial perturbations.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 120–129, September–October, 2000. 相似文献
6.
S. I. Gorlov 《Journal of Applied Mechanics and Technical Physics》2000,41(2):280-285
The nonlinear initial-boundary-value problem of a contour approaching an interface between two liquid media is considered.
A solution is constructed using a previously developed numerical method that is based on reducing the original problem to
a system of integrodifferential equations for singularities simulating liquid and rigid boundaries and a function that describes
the interface between the media. Calculation results for the perturbations generated by a circular cylinder approaching a
free surface are presented. The dependences of the flows obtained and the hydrodynamic characteristics of the contour on the
Froude number are estimated.
Omsk Branch of the Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, Omsk 644099. Translated
from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 84–89, March–April, 2000. 相似文献
7.
I. F. Shaikhislamov 《Journal of Applied Mechanics and Technical Physics》2000,41(2):212-219
The nonlinear problem of charge exchange between an ion flow and neutral particles is considered. An exact solution of the
equations of charge-exchange interaction in plane geometry is found. Parameters determining the effectiveness of interpenetration
of dense flows and the structure of the layer of intense interaction are obtained.
Institute of Laser Physics, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No.
2, pp. 11–19, March–April, 2000. 相似文献
8.
V. D. Bondar' 《Journal of Applied Mechanics and Technical Physics》2000,41(1):120-130
For materials characterized by a linear relation between Almansi strains and Cauchy stresses, relations between stresses and
complex potentials are obtained and the plane static problem of the theory of elasticity is thus reduced to a boundary-value
problem for the potentials. The resulting relations are nonlinear in the potentials; they generalize well-known Kolosov's
formulas of linear elasticity. A condition under which the results of the linear theory of elasticity follow from the nonlinear
theory considered is established. An approximate solution of the nonlinear problem for the potentials is obtained by the small-parameter
method, which reduces the problem to a sequence of linear problems of the same type, in which the zeroth approximation corresponds
to the problem of linear elasticity. The method is used to obtain both exact and approximate solutions for the problem of
the extension of a plate with an elliptic hole. In these solutions, the behavior of stresses on the hole contour is illustrated
by graphs.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41,
No. 1, pp. 133–143, January–February, 2000. 相似文献
9.
N. I. Makarenko 《Journal of Applied Mechanics and Technical Physics》1999,40(2):249-257
The problem of steady-state flows in a layer of a continuously stratified fluid is considered. The sufficient condition of
existence of families of shear flows that are consistent with the meaning of the laws of conservation of mass, momentum, and
energy with a uniform flow is given. Approximate solutions of the smooth-bore type, which describe the wave transitions for
pairs of conjugate flows of the first spectral mode, are obtained.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 69–78. March–April, 1999. 相似文献
10.
V. A. Saraikin 《Journal of Applied Mechanics and Technical Physics》1999,40(5):903-907
Equations are derived for stress concentration near a crack of closed contour lying in a plane. A system of one-dimensional
integral equations for the concentration factor is obtained. The right sides of the equations contain the initial approximation—a
solution of the problem of a circular crack whose sides are acted upon by nonaxisymmetric loading.
Mining Institute, Siberian Division, Russian Academy of Sciences, Novosibirsk 630091. Translated from Prikladnaya Mekhanika
i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 143–148, September–October, 1999. 相似文献
11.
Yu. A. Bogan 《Journal of Applied Mechanics and Technical Physics》1999,40(4):727-729
A system of hypersingular equations for the title problem is constructed. Qualitative properties of the solution of this system
are discussed.
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. 195–197, July–August, 1999. 相似文献
12.
We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov–Darwin (RVD) system globally in time. A similar result is claimed in Seehafer (Commun Math Sci 6:749–769, 2008) following the work in Pallard (Int Mat Res Not 57191:1–31, 2006). Our proof does not require estimates derived from the conservation of the total energy, nor those previously given on the transversal component of the electric field. These estimates are crucial in the references cited above. Instead, we exploit the formulation of the RVD system in terms of the generalized space and momentum variables. By doing so, we produce a simple a priori estimate on the transversal component of the electric field. We widen the functional space required for the Cauchy datum to extend the solution globally in time, and we improve decay estimates given in Seehafer (2008) on the electromagnetic field and its space derivatives. Our method extends the constructive proof presented in Rein (Handbook of differential equations: evolutionary equations, vol 3. Elsevier, Amsterdam, 2007) to solve the Cauchy problem for the Vlasov–Poisson system with a small initial datum. 相似文献
13.
V. N. Maksimenko G. V. Nedogibchenko 《Journal of Applied Mechanics and Technical Physics》2000,41(3):569-575
A mixed problem of linear elasticity for an infinite anisotropic plate with cuts and thin undeformable inclusions located
along arbitrary open smooth curves is solved with the use of complex potentials. Special representations of the solutions
are constructed and a governing system of singular integral equations is obtained. A numerical algorithm for determining the
stress-strain state of the plate, including the stress-intensity factors at the tips of cuts and rigid inclusions, is proposed.
Calculation results are given.
Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika,
Vol. 41, No. 3, pp. 213–219, May–June, 2000. 相似文献
14.
A solution of an initial-boundary-value problem for a system of integrodifferential equations which describes the plane waves
excited in an initially stationary heavy two-layer ideal fluid by a cylinder moving at an angle to the horizontal is investigated.
The homogeneous fluid fractions of different densities are assumed to be separated by an evolving fluid interface (horizontal
plane, if the liquid is at rest). An approximate solution of two problems for the waves excited by a cylinder moving with
a constant acceleration and an oscillating cylinder is constructed analytically.
Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–152, July–August,
1998. 相似文献
15.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》1998,39(5):699-709
The problem of the decay of an arbitrary discontinuity (the Riemann problem) for the system of equations describing vortex
plane-parallel flows of an ideal incompressible liquid with a free boundary is studied in a long-wave approximation. A class
of particular solutions that correspond to flows with piecewise-constant vorticity is considered. Under certain restrictions
on the initial data of the problem, it is proved that this class contains self-similar solutions that describe the propagation
of strong and weak discontinuities and the simple waves resulting from the nonlinear interaction of the specified vortex flows.
An algorithm for determining the type of resulting wave configurations from initial data is proposed. It extends the known
approaches of the theory of one-dimensional gas flows to the case of substantially two-dimensional flows.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 55–66, September–October, 1998. 相似文献
16.
M. V. Mir-Salim-zade 《Journal of Applied Mechanics and Technical Physics》2007,48(4):562-570
The fracture mechanics problem of crack initiation in a stiffened plate is considered. The crack nucleus is modeled by a prefracture
zone with bonds between the crack faces, which is treated as a region of weakened interparticle bonds of the material. The
boundary-value problem of the equilibrium of a stiffened plate with a crack nucleus reduces to a nonlinear singular integrodifferential
equation with a Cauchy type kernel. The strains in the crack initiation zone are found by solving this equation. The case
of the stress state of the plate with a periodic system of prefracture zones is considered.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 111–120, July–August, 2007. 相似文献
17.
B. N. Elemesova 《Journal of Applied Mechanics and Technical Physics》1999,40(1):28-35
The plane-parallel unsteady-state shear gas flow in a narrow channel of constant cross section is considered. The existence
theorem of solutions in the form of simple waves of a set of equations of motion is proved for a class of isentropic flows
with a monotone velocity profile over the channel depth. The exact solution described by incomplete beta-functions is found
for a polytropic equation of state in a class of isentropic flows.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 36–43, January–February, 1999. 相似文献
18.
O. I. Kocherha 《Nonlinear Oscillations》2007,10(2):246-256
We prove the asymptotic character of a solution of the Cauchy problem for a singularly perturbed linear system of differential
equations with degenerate matrix of the coefficients of derivatives in the case where the limit matrix pencil is regular and
has multiple “finite” and “infinite” elementary divisors. We establish conditions under which the constructed formal solutions
are asymptotic expansions of the corresponding exact solutions.
__________
Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 247–257, April–June, 2007. 相似文献
19.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》1998,39(1):12-23
An approximate system of equations that describe unsteady flow of an inviscid non-heat-conducting gas in a narrow channel
of varying area is derived. Generalized characteristics and hyperbolicity conditions are obtained for this system of equations.
In connection with characteristics theory, the average Mach number and the flow criticality condition are introduced. Exact
solutions that describe steady transonic channel flows are investigated.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 15–27, January–February, 1998. 相似文献
20.
V. D. Bondar’ 《Journal of Applied Mechanics and Technical Physics》1999,40(2):360-366
The relations of the nonlinear model of the theory of elasticity are considered. The Cauchy and the strain gradient tensors
are taken to be the characteristics of the stress-strain state of a body. Sufficient conditions under which the static equations
of elasticity are of elliptic type are established. These conditions are expressed in the form of constraints imposed on the
derivatives of the elastic potential with respect to the strain-measure characteristics. The cases of anisotropic and isotropic
bodies are treated, including the case where the Almansi tensor is taken to be the strain measure. The plane strain of a body
is investigated using actual-state variables.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40,
No. 2, pp. 196–203, March–April, 1999. 相似文献