共查询到9条相似文献,搜索用时 15 毫秒
1.
M. F. El-Sayed 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(1):19-39
In this paper, we consider the instability of the interface between two superposed streaming conducting and dielectric fluids
of finite depths through porous medium in a vertical electric field varying periodically with time. A damped Mathieu equation
with complex coefficients is obtained. The method of multiple scales is used to obtain an approximate solution of this equation,
and then to analyze the stability criteria of the system. We distinguish between the non-resonance case, and the resonance
case, respectively. It is found, in the first case, that both the porosity of porous medium, and the kinematic viscosities
have stabilizing effects, and the medium permeability has a destabilizing effect on the system. While in the second case,
it is found that each of the frequency of the electric field, and the fluid velocities, as well as the medium permeability,
has a stabilizing effect, and decreases the value of the resonance point, while each of the porosity of the porous medium,
and the kinematic viscosities has a destabilizing effect, and increases the value of the resonance point. In the absence of
both streaming velocities and porous medium, we obtain the canonical form of the Mathieu equation. It is found that the fluid
depth and the surface tension have a destabilizing effect on the system. This instability sets in for any value of the fluid
depth, and by increasing the depth, the instability holds for higher values of the electric potential; while the surface tension
has no effect on the instability region for small wavenumber values. Finally, the case of a steady electric field in the presence
of a porous medium is also investigated, and the stability conditions show that each of the fluid depths and the porosity
of the porous medium ɛ has a destabilizing effect, while the fluid velocities have stabilizing effect. The stability conditions
for two limiting cases of interest, the case of purely fluids), and the case of absence of streaming, are also obtained and
discussed in detail. 相似文献
2.
邹启苏 《应用数学和力学(英文版)》1982,3(2):255-265
The slow modulation of the interfacial capillary — gravity waves of two superposed fluids with uniform depths and solid walls is investigated by using the method of multiple scales. The evolution of a packet is described by the nonlinear Schrödinger equation, and then the stability of the so-called Stokes wave train is discussed. 相似文献
3.
M. F. El-Sayed 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(11):717-732
Summary The electrohydrodynamic Kelvin–Helmholtz instability of the interface between two uniform superposed viscoelastic (B′ model)
dielectric fluids streaming through a porous medium is investigated. The considered system is influenced by applied electric
fields acting normally to the interface between the two media, at which there are no surface charges present. In the absence
of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by either streaming
and applied electric fields for the potentially unstable configuration, or streaming only for the potentially stable configuration,
as long as perturbations in the direction of streaming are ignored. For perturbations in all other directions, there exists
instability for a certain wavenumber range. The instability of this system can be enhanced (increased) by normal electric
fields. In the presence of surface tension, it is found also that the normal electric fields have destabilizing effects, and
that the surface tension is able to suppress the Kelvin–Helmholtz instability for small wavelength perturbations, and the
medium porosity reduces the stability range given in terms of the velocities difference and the electric fields effect. Finally,
it is shown that the presence of surface tension enhances the stabilizing effect played by the fluid velocities, and that
the kinematic viscoelasticity has a stabilizing as well as a destabilizing effect on the considered system under certain conditions.
Graphics have been plotted by giving numerical values to the parameters, to depict the stability characteristics.
Received 27 March 2000; accepted for publication 3 May 2001 相似文献
4.
A.M. Khludnev A.A. Novotny J. Sokoowski A. ochowski 《Journal of the mechanics and physics of solids》2009,57(10):1718-1732
We consider an elastic body with a rigid inclusion and a crack located at the boundary of the inclusion. It is assumed that nonpenetration conditions are imposed at the crack faces which do not allow the opposite crack faces to penetrate each other. We analyze the variational formulation of the problem and provide shape and topology sensitivity analysis of the solution in two and three spatial dimensions. The differentiability of the energy with respect to the crack length, for the crack located at the boundary of rigid inclusion, is established. 相似文献
5.
We consider the problem of two- and three-dimensional nonlinear buoyant flows in horizontal mushy layers during the solidification of binary alloys. We study the nonlinear evolution of such flow based on a recently developed realistic model for the mushy layer with permeable interface. The evolution approach is based on a Landau type equation for the amplitude of the secondary nonlinear solution, which can be in the form of rolls, squares, rectangles or hexagons. Using both analytical and computational methods, we calculate the solutions to the evolution equation near the onset of motion for both subcritical and supercritical regimes and determine the stable solutions. We find, in particular, that for several investigated cases with different parameter regimes, secondary solution in the form of subcritical down-hexagons or supercritical up-hexagons can be stable. However, the preferred solution for smallest values of the Rayleigh number and the amplitude of motion is in the form of subcritical down-hexagons. This result appears to agree with the experimental observation on the form of the convective flow near the onset of motion. 相似文献
6.
The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids.The propagation of three longitudinal waves is represented through three scalar potential functions.The lone transverse wave is presented by a vector potential function.The displacements of particles in different phases of the aggregate are defined in terms of these potential functions.It is shown that there exist three longitudinal waves and one transverse wave.The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated.For the presence of viscosity in pore-fluids,the waves refracted to the porous medium attenuate in the direction normal to the interface.The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations.These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave.The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model.The conservation of the energy across the interface is verified.The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed. 相似文献
7.
研究了中心力场中的一类刚-弹耦合系统的平面运动动力学,模型是带有一悬臂
梁的刚体. 综合考虑了系统轨道运动与姿态运动,在Lagrange力学体系下给出了系统的运
动方程,在保守系统和考虑梁的材料黏滞阻尼两种情况下,利用能量-动量方法给出了一类
相对平衡点稳定性的充分条件. 相似文献
8.
The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus voltage are considered to maintain two fluctuations in the amplitude and phase angle. The case of 1:3 internal resonance between the two modes in the presence of parametric principal resonance is considered and examined. The method of multiple scales is used to obtain the bifurcation equations of this system. Then, by employing the singularity method, the transition sets determining different bifurcation patterns of the system are obtained and analyzed, which reveal the effects of the infinite-bus voltage amplitude and phase fluctuations on bifurcation patterns of this system. Finally, the bifurcation patterns are all examined by bifurcation diagrams. The results obtained in this paper will contribute to a better understanding of the complex nonlinear dynamic behaviors in a two-machine infinite-bus (TMIB) power system. 相似文献