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1.
Triple shock-wave configurations in steady supersonic flows of an inviscid perfect gas are considered. Triple configurations
with special intensities of shock waves and extreme ratios of various flow parameters behind these configurations are determined.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 39–53, July–August, 2006. 相似文献
2.
A. V. Belimov G. I. Dudnikova M. P. Fedoruk É. P. Shurina 《Journal of Applied Mechanics and Technical Physics》1999,40(4):551-557
Numerical models describing the formation of equilibrium “Belt”-type plasma configurations using direct discharge are developed.
The magnetobaric characteristics p (ψ) of these configurations are determined. The calculation results are in agreement with
experimental data.
Institute of Computational Technologies, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 3–10, July – August, 1999. 相似文献
3.
We present an exact solution for the postbuckling configurations of beams with fixed–fixed, fixed–hinged, and hinged–hinged
boundary conditions. We take into account the geometric nonlinearity arising from midplane stretching, and as a result, the
governing equation exhibits a cubic nonlinearity. We solve the nonlinear buckling problem and obtain a closed-form solution
for the postbuckling configurations in terms of the applied axial load. The critical buckling loads and their associated mode
shapes, which are the only outcome of solving the linear buckling problem, are obtained as a byproduct. We investigate the
dynamic stability of the obtained postbuckling configurations and find out that the first buckled shape is a stable equilibrium
position for all boundary conditions. However, we find out that buckled configurations beyond the first buckling mode are
unstable equilibrium positions. We present the natural frequencies of the lowest vibration modes around each of the first
three buckled configurations. The results show that many internal resonances might be activated among the vibration modes
around the same as well as different buckled configurations. We present preliminary results of the dynamic response of a fixed–fixed
beam in the case of a one-to-one internal resonance between the first vibration mode around the first buckled configuration
and the first vibration mode around the second buckled configuration. 相似文献
4.
Juhi Jang 《Archive for Rational Mechanics and Analysis》2010,195(3):797-863
We establish the local-in-time well-posedness of strong solutions to the vacuum free boundary problem of the compressible
Navier–Stokes–Poisson system in the spherically symmetric and isentropic motion. Our result captures the physical vacuum boundary
behavior of the Lane–Emden star configurations for all adiabatic exponents
g < \frac65{\gamma < \frac{6}{5}} . 相似文献
5.
Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier-Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence-divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone. 相似文献
6.
DNA molecules in the familiar Watson–Crick double helical B form can be treated as though they have rod-like structures obtained
by stacking dominoes one on top of another with each rotated by approximately one-tenth of a full turn with respect to its
immediate predecessor in the stack. These “dominoes” are called base pairs. A recently developed theory of sequence-dependent DNA elasticity (Coleman, Olson, & Swigon, J. Chem. Phys. 118:7127–7140, 2003) takes into account the observation that the step from one base pair to the next can be one of several
distinct types, each having its own mechanical properties that depend on the nucleotide composition of the step. In the present
paper, which is based on that theory, emphasis is placed on the fact that, as each base in a base pair is attached to the
sugar-phosphate backbone chain of one of the two DNA strands that have come together to form the Watson–Crick structure, and
each phosphate group in a backbone chain bears one electronic charge, two such charges are associated with each base pair,
which implies that each base pair is subject to not only the elastic forces and moments exerted on it by its neighboring base
pairs but also to long range electrostatic forces that, because they are only partially screened out by positively charged
counter ions, can render the molecule’s equilibrium configurations sensitive to changes in the concentration c of salt in the medium. When these electrostatic forces are taken into account, the equations of mechanical equilibrium for
a DNA molecule with N + 1 base pairs are a system of μN non-linear equations, where μ, the number of kinematical variables describing the relative displacement and orientation of adjacent pairs is in general
6; it reduces to 3 when base-pair steps are assumed to be inextensible and non-shearable. As a consequence of the long-range
electrostatic interactions of base pairs, the μN × μN Jacobian matrix of the equations of equilibrium is full. An efficient numerically stable computational scheme is here presented
for solving those equations and determining the mechanical stability of the calculated equilibrium configurations. That scheme
is employed to compute and analyze bifurcation diagrams in which c is the bifurcation parameter and to show that, for an intrinsically curved molecule, small changes in c can have a strong effect on stable equilibrium configurations. Cases are presented in which several stable configurations
occur at a single value of c.
相似文献
7.
The length scale criteria is widely accepted as an explanation for transition and hence existence of different shock wave
reflection configurations in pseudo-steady flows. However, there has not been any attempt to validate this criteria using
information obtained from a time-dependent numerical simulation. A high resolution time-dependent numerical simulation in
pseudo-steady flow is carried out in the present work. Time-dependent numerical data is used to calculate flow features in
a laboratory frame of reference to verify validity of the length scale criteria for existence of different shock wave reflection
configurations in pseudo-steady flow. This analysis is then extended to the study of unsteady shock wave reflection configurations
in shock–vortex interactions. It is shown that the existence of regular reflection (RR) and Mach reflection (MR) configurations
in an unsteady flowfield resulting from shock–vortex interactions can also be explained locally based on limiting conditions
similar to that prescribed by the length scale criteria for pseudo-steady flow.
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8.
Eduardo S. G. Leandro 《Archive for Rational Mechanics and Analysis》2003,167(2):147-177
We consider here the classical question of finiteness (see Smale [13] and Wintner [15]) – given n point masses, is the corresponding number of central configurations finite? We prove finiteness for a particular family of
d-dimensional symmetrical configurations of d+2 point masses. Also, we study the bifurcations of these configurations and provide the exact number of central configurations
when d=2, 3. All our results stem from the application of a new method for studying symmetrical classes of central configurations,
which is presented in this work.
(Accepted September 23, 2002) Published online February 14, 2003
Communicated by P. Rabinowitz 相似文献
9.
Stress Generated During Drying of Saturated Porous Media 总被引:1,自引:0,他引:1
The article is a contribution for the modelling of heat and mass transfers coupled to strain–stress equations during drying
of deformable two-phase media. Both unidirectional and bidirectional configurations are examined. In order to compare the
results, one assumes the material of a convectively dried clay slab in two configurations. Numerical calculations of the temperature,
drying curves variations and the spatio-temporal distributions of moisture, temperature and drying induced stresses are evaluated.
A significant difference was observed between the results obtained for both configurations particularly in intensity of the
shear stress that caused cracking. 相似文献
10.
The equation of state of finite-strain thermoelasticity is obtained using a formalized approach to constructing constitutive
relations for complex media under the assumption of closeness of intermediate and current configurations. A variational formulation
of the coupled thermoelastic problem is proposed. The constitutive equation, the heat-conduction equation, the relations for
internal energy, free energy, and entropy, and the variational formulation of the coupled problem of finite-strain thermoelasticity
are tested on the problem of uniaxial extension of a bar. The model adequately describes experimental data for elastomers,
such as entropic elasticity, temperature inversion, and temperature variation during an adiabatic process.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 184–196, May–June, 2008. 相似文献
11.
P. Taheri A. S. Rana M. Torrilhon H. Struchtrup 《Continuum Mechanics and Thermodynamics》2009,21(6):423-443
Four basic flow configurations are employed to investigate steady and unsteady rarefaction effects in monatomic ideal gas
flows. Internal and external flows in planar geometry, namely, viscous slip (Kramer’s problem), thermal creep, oscillatory
Couette, and pulsating Poiseuille flows are considered. A characteristic feature of the selected problems is the formation
of the Knudsen boundary layers, where non-Newtonian stress and non-Fourier heat conduction exist. The linearized Navier–Stokes–Fourier
and regularized 13-moment equations are utilized to analytically represent the rarefaction effects in these boundary-value
problems. It is shown that the regularized 13-moment system correctly estimates the structure of Knudsen layers, compared
to the linearized Boltzmann equation data. 相似文献
12.
Highly porous two-dimensional (2D) cellular metals have multifunctional attributes, with tailorable structures to achieve
multifunctional performance. The focus of this study is to explore the optimal cellular topology of 2D cellular metals for
heat dissipation, and to investigate the eligibility of different heat enhancement techniques for more efficient heat dissipation.
An analytical approach for the optimal design of metallic 2D cellular materials, cooled by single-phase laminar forced convection
in various flow configurations, is proposed and validated by comparison with full numerical simulations. The optimal design
is characterized by two subsidiary dimensionless parameters: one reflecting the trade-off between convection and fluid friction,
and the other reflecting the optimal balance between conduction and convection. A heat transfer enhancement technique––boundary
layer redevelopment––is subsequently introduced and its feasibility examined experimentally. Future research directions in
specific areas are discussed. 相似文献
13.
A system consisting of two linearly coupled chaotic Colpitts oscillators is considered. Two different coupling configurations,
namely coupled collector nodes (C–C) and coupled emitter nodes (E–E) have been investigated. In addition to identical oscillators
the case of mismatched circuits has been studied. Specifically the influence of the transistor parameter mismatch has been
analyzed. The relative synchronization error has been estimated for different mismatch levels provided the coupling coefficient
is twice larger than the synchronization threshold. Illustrative experimental results, including phase portraits and synchronization
error are presented. 相似文献
14.
In this study, non-Darcy inertial two-phase incompressible and non-stationary flow in heterogeneous porous media is analyzed
using numerical simulations. For the purpose, a 3D numerical tool was fully developed using a finite volume formulation, although
for clarity, results are presented in 1D and 2D configurations only. Since a formalized theoretical model confirmed by experimental
data is still lacking, our study is based on the widely used generalized Darcy–Forchheimer model. First, a validation is performed
by comparing numerical results of the saturation front kinetics with a semi-analytical solution inspired from the Buckley–Leverett
model extended to take into account inertia. Second, we highlight the importance of inertial terms on the evolution of saturation
fronts as a function of a suitable Reynolds number. Saturation fields are shown to have a structure markedly different from
the classical case without inertia, especially for heterogeneous media, thereby, emphasizing the necessity of a more complete
model than the classical generalized Darcy’s one when inertial effects are not negligible. 相似文献
15.
This large eddy simulation (LES) study is applied to three different premixed turbulent flames under lean conditions at atmospheric
pressure. The hierarchy of complexity of these flames in ascending order are a simple Bunsen-like burner, a sudden-expansion
dump combustor, and a typical swirl-stabilized gas turbine burner–combustor. The purpose of this paper is to examine numerically
whether the chosen combination of the Smagorinsky turbulence model for sgs fluxes and a novel turbulent premixed reaction
closure is applicable over all the three combustion configurations with varied degree of flow and turbulence. A quality assessment
method for the LES calculations is applied. The cold flow data obtained with the Smagorinsky closure on the dump combustor
are in close proximity with the experiments. It moderately predicts the vortex breakdown and bubble shape, which control the
flame position on the double-cone burner. Here, the jet break-up at the root of the burner is premature and differs with the
experiments by as much as half the burner exit diameter, attributing the discrepancy to poor grid resolution. With the first
two combustion configurations, the applied subgrid reaction model is in good correspondence with the experiments. For the
third case, a complex swirl-stabilized burner–combustor configuration, although the flow field inside the burner is only modestly
numerically explored, the level of flame stabilization at the junction of the burner–combustor has been rather well captured.
Furthermore, the critical flame drift from the combustor into the burner was possible to capture in the LES context (which
was not possible with the RANS plus k–ɛ model), however, requiring tuning of a prefactor in the reaction closure. 相似文献
16.
The Newtonian circular restricted four-body problem is considered. We obtain nonlinear algebraic equations determining equilibrium
solutions in the rotating frame and find six possible equilibrium configurations of the system. Studying the stability of
equilibrium solutions, we prove that the radial equilibrium solutions are unstable, while the bisector equilibrium solutions
are stable in Lyapunov’s sense if the mass parameter satisfies the conditions μ ∈ (0, μ0, where μ0 is a sufficiently small number, and μ ≠ μj, j = 1, 2, 3. We also prove that, for μ = μ1 and μ = μ3, the resonance conditions of the third order and the fourth order, respectively, are satisfied and, for these values of μ,
the bisector equilibrium solutions are unstable and stable in Lyapunov’s sense, respectively. All symbolic and numerical calculations
are done with the Mathematica computer algebra system.
Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 66–82, January–March, 2007. 相似文献
17.
An experimental investigation is conducted to bring out the effects of coolant injector configuration on film cooling effectiveness,
film cooled length and film uniformity associated with gaseous and liquid coolants. A series of measurements are performed
using hot air as the core gas and gaseous nitrogen and water as the film coolants in a cylindrical test section simulating
a thrust chamber. Straight and compound angle injection at two different configurations of 30°–10° and 45°–10° are investigated
for the gaseous coolant. Tangential injection at 30° and compound angle injection at 30°–10° are examined for the liquid coolant.
The analysis is based on measurements of the film-cooling effectiveness and film uniformity downstream of the injection location
at different blowing ratios. Measured results showed that compound angle configuration leads to lower far-field effectiveness
and shorter film length compared to tangential injection in the case of liquid film cooling. For similar injector configurations,
effectiveness along the stream wise direction showed flat characteristics initially for the liquid coolant, while it was continuously
dropping for the gaseous coolant. For liquid coolant, deviations in temperature around the circumference are very low near
the injection point, but increases to higher values for regions away from the coolant injection locations. The study brings
out the existance of an optimum gaseous film coolant injector configuration for which the effectiveness is maximum. 相似文献
18.
This paper presents a comparative-numerical investigation on film cooling from a row of simple and compound-angle holes injected
at 35° on a flat plate with four film cooling configurations: (1) cylindrical film hole; (2) 15° forward diffused film hole;
(3) trenched cylindrical film hole; (4) trenched 15° forward-diffused film hole. All simulations are at fixed density ratio
of 1.6, blowing ratio of 1.25, length-to-diameter L/D = 4 and pitch-to-diameter ratio of 3.0. The effect of length-to-diameter ratio on film cooling has been also investigated
using L/D in the range of 1–8. Computational solutions of the steady, Reynolds-averaged Navier–Stokes equations have been obtained
using a finite volume method. It has been found that the shape of the hole and the trenched holes can significantly affect
the film cooling flow over the protected surface. Further, it has been shown that the film cooling effectiveness by trenched
shaped holes is higher than all other configurations both in spanwise and streamwise specially downstream of the injection.
Also, a trenched compound angle injection shaped hole produces much higher film cooling protection than the other configurations
investigated in the present paper. The length-to-diameter ratio of trenched holes was found to have a significant effect on
film cooling effectiveness and the spread of the coolant jets. 相似文献
19.
An approximate analytical model for calculation of the parameters of a steady gas flow inside a plane constricting channel
formed by two symmetrically positioned wedges is suggested. A Mach configuration of shock waves (triple point) is formed in
the channel when the wedge angles are larger than some critical value. The flow calculation in a constricting channel reduces
to the solution of the iterative problem for a system of nonlinear algebraic equations. The configurations of shock waves,
the slipstream, and the sonic line are described by the proposed model of a gas flow. A comparison of the results obtained
using this model allows a fairly accurate calculation of the Mach stem and the length of the subsonic-flow region.
Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated
from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 52–58, May–June, 1998. 相似文献
20.
This paper is first of the two papers dealing with analytical investigation of resonant multi-modal dynamics due to 2:1 internal
resonances in the finite-amplitude free vibrations of horizontal/inclined cables. Part I deals with theoretical formulation
and validation of the general cable model. Approximate nonlinear partial differential equations of 3-D coupled motion of small
sagged cables – which account for both spatio-temporal variation of nonlinear dynamic tension and system asymmetry due to
inclined sagged configurations – are presented. A multi-dimensional Galerkin expansion of the solution of nonplanar/planar
motion is performed, yielding a complete set of system quadratic/cubic coefficients. With the aim of parametrically studying
the behavior of horizontal/inclined cables in Part II [25], a second-order asymptotic analysis under planar 2:1 resonance
is accomplished by the method of multiple scales. On accounting for higher-order effects of quadratic/cubic nonlinearities,
approximate closed-form solutions of nonlinear amplitudes, frequencies and dynamic configurations of resonant nonlinear normal
modes reveal the dependence of cable response on resonant/nonresonant modal contributions. Depending on simplifying kinematic
modeling and assigned system parameters, approximate horizontal/inclined cable models are thoroughly validated by numerically
evaluating statics and non-planar/planar linear/non-linear dynamics against those of the exact model. Moreover, the modal
coupling role and contribution of system longitudinal dynamics are discussed for horizontal cables, showing some meaningful
effects due to kinematic condensation. 相似文献