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1.
The paper deals with the existence of positive (nonnegative) solutions of linear homogeneous impulsive differential equations.
The main result is also applied to the investigation of a similar problem for higher-order linear homogeneous impulsive differential
equations. All results are formulated in terms of coefficients of the equations.
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Published in Neliniini Kolyvannya, Vol. 8, No. 3, pp. 291–297, July–September, 2005. 相似文献
2.
It is known that the three-dimensional Navier–Stokes system for an incompressible fluid in the whole space has a one parameter
family of explicit stationary solutions that are axisymmetric and homogeneous of degree −1. We show that these solutions are
asymptotically stable under any L
2-perturbation. 相似文献
3.
Axisymmetric contact problem of cubic quasicrystalline materials 总被引:3,自引:0,他引:3
The axisymmetric elasticity theory of cubic quasicrystal was developed in Ref. [1]. The axisymmetric elasticity problem of
cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function,
based on which, the exact analytic solutions for the elastic field of an axisymmetric contact problem of cubic quasicrystalline
materials are obtained for universal contact stress or contact displacement. The result shows that if the contact stress has
order −1/2 singularity on the edge of the contact domain, the contact displacement is a constant in the contact domain. Conversely,
if the contact displacement is a constant, the contact stress must have order −1/2 singularity on the edge of the contact
domain.
Project supported by the National Natural Science Foundation of China (No. 19972011). 相似文献
4.
《International Journal of Solids and Structures》2005,42(14):4115-4153
Transient wave propagation of isotropic thin plates using a higher-order plate theory is presented in this paper. The aim of this investigation is to assess the applicability of the higher-order plate theory in describing wave behavior of isotropic plates at higher frequencies. Both extensional and flexural waves are considered. A complete discussion of dispersion of isotropic plates is first investigated. All the wave modes and wave behavior for each mode in the low and high-frequency ranges are provided in detail. Using the dispersion relation and integral transforms, exact integral solutions for an isotropic plate subjected to pure impulse load and a number of wave excitations based on the higher-order theory are obtained and asymptotic solutions which highlight the physics of waves are also presented. The axisymmetric three-dimensional analytical solutions of linear wave equations are also presented for comparison. Results show that the higher-order theory can predict the wave behavior closely with exact linear wave solutions at higher frequencies. 相似文献
5.
V. Sh. Shagapov M. K. Khasanov N. G. Musakaev 《Journal of Applied Mechanics and Technical Physics》2008,49(3):462-472
Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and
water are considered. Self-similar solutions of an axisymmetric problem, which describe the distributions of the basic parameters
in the reservoir, are constructed. The existence of solutions is demonstrated, which predict gas hydrate formation both on
the frontal surface and in the volume zone.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 137–150, May–June, 2008. 相似文献
6.
Aqueous solutions composed of dispersed nanoparticles and entangled polymers are shown to exhibit common viscoelasticity over a range of particle and polymer concentrations. Time–temperature superposition and time–concentration superposition are applied to generate rheological master curves for neat and laponite-filled aqueous solutions of poly(ethylene oxide). The shift factors were correlated in terms of temperature and concentration and are found to differ from previous reports for ideal polymer solutions, which can be rationalized with a molecular interpretation of the structure of the laponite–polymer solutions. Laponite addition to the concentrated polymer solution is observed to increase the relaxation time but decrease the elastic modulus, which is a consequence of polymer adsorption and bridging. The addition of small amounts of laponite to stable PEO–water solutions also leads to ageing on the time scale of days. 相似文献
7.
S. V. Khabirov 《Journal of Applied Mechanics and Technical Physics》2007,48(5):641-648
All partially invariant solutions in terms of the group of extensions for a model of radial motions of an ideal gas are found.
The solutions are obtained by the method of separation of variables in an equation containing functions of one variable but
different functions of different independent variables. The solutions predict different continuous unsteady convergence or
expansion of the gas under the action of a piston with a point sink or source. If the sink or source affects all particles
simultaneously, a collapse or an explosion occurs.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 26–34, September–October, 2007. 相似文献
8.
Summary This paper presents the solution of geometrically nonlinear problems in solid mechanics by the Domain-Boundary Element Method.
Because of the Total-Lagrange approach, the arising domain and boundary integrals are evaluated in the undeformed configuration.
Therefore, the system matrices remain unchanged during the solution procedure, and their time-consuming computation needs
to be performed only once. While the integral equations for axisymmetric finite deformation problems will be derived in detail,
the basic ideas of the formulation in two and three dimensions can be found in [1]. The present formulation includes torsional
problems with finite deformations, where additional terms arise due to the curvilinear coordinate system. A Newton–Raphson
scheme is used to solve the nonlinear set of equations. This involves the solution of a large system of linear equations,
which has been a very time-consuming task in former implementations, [1, 2]. In this work, an iterative solver, i.e. the generalized
minimum residual method, is used within the Newton–Raphson algorithm, which leads to a significant reduction of the computation
time. Finally, numerical examples will be given for axisymmetric and two/three-dimensional problems.
Received 29 August 2000; accepted for publication 10 October 2000 相似文献
9.
In the theory of nonlinear elasticity of rubber-like materials, if a homogeneous isotropic compressible material is described
by a strain–energy function that is a homogeneous function of the principal stretches, then the equations of equilibrium for axisymmetric deformations reduce to a separable
first-order ordinary differential equation. For a particular class of such strain–energy functions, this property is used
to obtain a general parametric solution to the equilibrium equation for plane strain bending of cylindrical sectors. Specification
of the arbitrary function that appears in such strain–energy functions yields some parametric solutions. In some cases, the
parameter can be eliminated to yield closed-form solutions in implicit or explicit form. Other possible forms for the arbitrary
constitutive function that are likely to yield such solutions are also indicated. 相似文献
10.
《Acta Mechanica Solida Sinica》2016,(5)
A refined theory of axisymmetric deformation of an isotropic poroelastic circular cylinder in a steady-state is presented directly by utilizing the general solutions and Lur'e method without any advance hypothesis.The refined equations are derived under non-homogenous boundary conditions,and the approximate solutions are obtained by omitting higher-order terms.The all-inclusive refined equations and approximate solutions constitute the refined theory of circular cylinders.Correlative examples are brought up to analyze influences of liquid-solid coupling properties on the mechanical behavior of poroelastic materials.Moreover,the present results are converted into those of homologous pure elastic problem directly. 相似文献
11.
S. V. Khabirov 《Journal of Applied Mechanics and Technical Physics》2009,50(2):207-212
This paper deals with one insufficiently studied submodel of invariant solutions of rank 1 of the equations of gas dynamics.
It is shown that, in cylindrical coordinates, the submodel without swirling reduces to a system of two ordinary differential
equations. For the equation of state with additional invariance, a self-similar system is obtained. A pattern of phase trajectories
is constructed, and particle motion is studied using asymptotic methods. The obtained solutions describe unsteady flows over
axisymmetric bodies with possible strong discontinuities.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 46–52, March–April, 2009. 相似文献
12.
Yu. N. Gordeev A. E. Sandakov Yu. L. Chizhov 《Journal of Applied Mechanics and Technical Physics》2008,49(5):776-780
A problem of piston-induced displacement of one gas by another in cracks (porous media) in an axisymmetric case with a quadratic
drag law is studied. Self-similar solutions for determining the dynamic characteristics (velocity and pressure) of the displacing
and displaced gases are constructed in quadratures. The velocity and pressure are studied as functions of a self-similar variable
for several initial conditions and parameters.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 87–92, September–October, 2008. 相似文献
13.
V. A. Batishchev 《Journal of Applied Mechanics and Technical Physics》1999,40(3):479-484
Thermocapillary flows of a fluid in a lamina with a rigid lower wall and a free upper surface, along which the temperature
gradient is given in the radial direction, are investigated for large Marangoni numbers. Self-similar solutions which describe
the axisymmetric flow regimes of a fluid without the circumferential velocity component are constructed numerically and asymptotically
for a system of Prandtl equations. It is shown that a pair of new self-similar flow regimes of a fluid with rotation branches
off from the regimes obtained. The new regimes ere calculated numerically and asymptotically.
Rostov State University, Rostov-on-Don 344090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No.
3, pp. 137–142, May–June, 1999. 相似文献
14.
L. I. Shkutin 《Journal of Applied Mechanics and Technical Physics》2008,49(2):330-335
A mathematical formulation is given of nonlinear axisymmetric buckling problems for plates and shells in the two-phase zones
of austenite-to-martensite transformation. Numerical solutions of the direct-and inverse-transformation problems are used
to construct hysteresis loops for thermomechanically cycled, pressure-loaded circular plates and shallow spherical domes of
titanium nickelide (NiTi) alloy. It is shown that dynamic instability of the dome deformation process can occur during transformation under loads notably
lower than the upper critical values for the isothermal states of the material outside the transformation zone. A theoretical
analysis gives external loads below which the dome remains stable in the thermally cycled material with phase transformations.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 204–210, March–April, 2008. 相似文献
15.
V. D. Bondar’ 《Journal of Applied Mechanics and Technical Physics》2009,50(2):352-359
The plane strain of an incompressible body is studied with geometrical and physical nonlinearity and potential forces taken
into account. A nonlinear system of equations for strains is obtained in actual variables, and conditions of its ellipticity
are derived in terms of the elastic potential. Boundary conditions for strains are found from specified loads. Analytical
solutions of the boundary problem in strains and their corresponding stress fields are found for the case of identical elongations.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 217–225, March–April, 2009 相似文献
16.
V. V. Pukhnachev 《Journal of Applied Mechanics and Technical Physics》2007,48(3):310-321
The equilibrium of a free weightless liquid film fixed over a planar contour and acted upon by thermocapillary forces is studied.
Trends in the behavior of free liquid films are important for understanding the processes occurring in foams. The equilibrium
equations for a nonisothermal weightless free film are derived for the two limiting cases: the temperature of the film is
considered a known function of the coordinates; the free surface of the film is thermally insulated. For the plane and axisymmetric
cases, the existence conditions for the solutions of the resulting nonlinear boundary-value problems are found and their properties
are studied. For the general case, an approximate solution of the equilibrium problem is obtained provided that the analogue
of the Marangoni number is small.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 16–29, May–June, 2007. 相似文献
17.
New analytical solutions for axisymmetric deformation of a viscous hollow circular cylinder on a rigid fibre are given. One
of the solutions generalizes the famous Prandtl’s solution for compression of a rigid perfectly plastic layer between two
rough, parallel plates and the other is a modification of Spencer’s solution for compression of an axisymmetric rigid perfectly
plastic layer on a rigid fibre. All equations are satisfied exactly whereas some boundary conditions are approximated in a
standard manner. Special attention is devoted to frictional interface conditions since these conditions result in additional
limitations of the applicability of the solution when compared to that based on a rigid perfectly plastic models. In particular,
difficulties with the convergence of numerical solutions under certain conditions can be explained with the use of results
obtained. Therefore, the solutions can serve as benchmark problems for verifying numerical codes. The solutions are also adopted
to predict the brittle fracture of fibres by means of an approach used in previous studies and confirmed by experiment. 相似文献
18.
The axisymmetric problem of the evolution of the free surface of a fluid during the filling of a toroidal vessel under conditions
of weightlessness is considered. Despite its interest [1, 2], this topical problem of the hydrodynamics of weightlessness
remains unsolved for lack of an effective method of solution. This paper employs the iteration-difference approach proposed
in [3–5] for calculating simply and doubly connected axisymmetric equilibrium figures.
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 154–156, November–December, 1986. 相似文献
19.
Yu. D. Shmyglevskii 《Fluid Dynamics》1998,33(2):298-300
Chains of coaxial vortex formations of the “vortex breakdown“ type in axisymmetric swirling incompressible viscous and ideal
fluid flows are represented in analytic form.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–176, March–April, 1998. 相似文献
20.
The stability of a surface-charged cylindrical jet in a longitudinal uniform electric field with respect to capillary pertubations
is investigated in the linear approximation. The evolution of both axisymmetric and azimuthal-periodic perturbations is analyzed.
In the latter case the first two modes among the azimuthal wavenumbers — bending and Bohr — are considered. Axisymmetric and
bending instabilities lead to the transverse disintegration of the jet into individual drops and the Bohr mode to the longitudinal
separation of the input jet into two parts. It is found that the axisymmetric and bending instabilities, respectively, can
be completely suppressed and significantly attenuated by means of an external longitudinal field. In this case the role of
the Bohr mode becomes more important leading under certain conditions to longitudinal longwave jet splitting. Events which
can be interpreted as manifestations of longitudinal partition of the jet (dumbbell-like cross-section, branching nodes) are
observed in experiments with evaporating polymer-solution microjets.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 29–40, March–April, 1998.
The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 97-01-00153). 相似文献