共查询到20条相似文献,搜索用时 31 毫秒
1.
Jean-Jacques Sinou 《International Journal of Non》2007,42(7):959-972
The stability of a rotor system presenting a transverse breathing crack is studied by considering the effects of crack depth, crack location and the shaft's rotational speed. The harmonic balance method, in combination with a path-following continuation procedure, is used to calculate the periodic response of a non-linear model of a cracked rotor system. The stability of the rotor's periodic movements is studied in the frequency domain by introducing the effects of a perturbation on the periodic solution for the cracked rotor system.It is shown that the areas of instability increase considerably when the crack deepens, and that the crack's position and depth are the main factors affecting not only the non-linear behaviour of the rotor system but also the different zones of dynamic instability in the periodic solution for the cracked rotor. The effects of some other system parameters (including the disk position and the stiffness of the supports) on the dynamic stability of the non-linear periodic response of the cracked rotor system are also investigated. 相似文献
2.
A. V. Kuznetsov 《Theoretical and Computational Fluid Dynamics》2006,20(2):73-87
This paper investigates the effect of vertical vibration on the stability of a dilute suspension of oxytactic microorganisms
in a shallow horizontal fluid layer. For the case of high-frequency vibration, an averaging method is utilized to derive the
equations describing the mean flow by decomposing the solutions of governing equations into two components: one that varies
slowly with time, and a second that varies rapidly with time. Linear stability analysis is used to investigate the stability
of the obtained averaged equations. It is predicted that high-frequency, low-amplitude vertical vibration has a stabilizing
effect on a suspension of oxytactic microorganisms confined in a shallow horizontal layer.
PACS 47.27 Te; 68.60 Dv 相似文献
3.
Until now, an unconditional nonlinear energy stability analysis for thermal convection according to Navier-Stokes theory had not been developed for the case in which the viscosity depends on the temperature in a quadratic manner such that the viscosity has a maximum. We analyse here a model of non-Newtonian fluid behaviour that allows us to develop an unconditional analysis directly when the quadratic viscosity relation is allowed. By unconditional, we mean that the nonlinear stability so obtained holds for arbitrarily large perturbations of the initial data. The nonlinear stability boundaries derived herein are sharp when compared with the linear instability thresholds.Received: 9 April 2003, Accepted: 28 April 2003, Published online: 12 December 2003PACS:
03.50.De, 04.20.-q, 42.65.-kCorrespondence to B. Straughan 相似文献
4.
The energy method is used to analyze the viscoelastic fluid convection problem in a thin horizontal layer, subjected to an applied inclined temperature gradient. The boundaries are considered to be rigid and perfectly conducting. Both linear and nonlinear stability analyses are carried out. The eigenvalue problem is solved by the Chebyshev Tau-QZ method and comparisons are reported between the results of the linear theory and energy stability theory.Received: 12 March 2004, Accepted: 19 April 2004, Published online: 17 September 2004PACS:
47.20 Ky, 47-27 Te, 83.60 Wc
Correspondence to: P.N. Kaloni 相似文献
5.
Liu Yanzhu 《Acta Mechanica Sinica》1987,3(3):278-285
In the present paper the stability of permanent rotation of a symmetric top rotating on a slightly rough horizontal plane
about the erect polar or transverse axis is discussed via the perturbation method. As a perturbation factor, the frictional
force is an arbitrary nonlinear function of the sliding velocity. The same stability criterion as that in the Contensou-Magnus
linear theory is obtained, but the hypothesis of the linearity for friction can be omitted. It shows that the direction of
the sliding velocity at the contact point is an important factor, which influences the stability of the top. And then an explicit
physical explanation is given. 相似文献
6.
This study investigates secondary instabilities of periodic wakes of a circular cylinder with infinitely long span. It has been known that after the wake undergoes a supercritical Hopf bifurcation (the primary instability) that leads to two-dimensional von Kantian vorlex street, the secondary instability occurs sequentially, which results in the onset of three-dimensional flow. Williamson (1996) has reviewed that the periodic wakes over a range of moderate Reynolds number from 140 to 300 are characterized by two critical modes. Mode A and Mode B, which are respectively associated with large-scale and fine-scale structures in span. In order to understand a sequence of bifurcation in transitional wake, in this paper, the stability of periodic Row governed by the linearized Navier-Stokes equations is analyzed by using the Floquet stability theory. By employing the finite elemental discretization with a fine mesh, the numerical results for both simulation and stability analysis have high spatio-resolution. The obtained stability results are in good agreement with experimental data and some relevant numerical results. By means of visualizations of the three-dimensionally critical flow structures. the existence of Mode A and Mode B is verified from the spatial structures in both the two modes. 相似文献
7.
In this paper, a theoretical investigation of nonlinear vibrations of a 2 degrees of freedom system when subjected to saturation
is studied. The method has been especially applied to a system that consists of a DC motor with a nonlinear controller and
a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. It is shown that the closed-loop
system exhibits different response regimes. The nature and stability of these regimes are studied and the stability boundaries
are obtained. The effects of the initial conditions on the response of the system have also been investigated. Furthermore,
the second-order solution is presented and the corresponding results are compared with those of the first-order solution.
It is shown that by increasing the amplitude of the excitation voltage, the higher-order term in the solution becomes significant
and causes a drift in the response. In order to verify the obtained theoretical results, they are compared with the corresponding
numerical results. Good agreement between the two sets of results is observed. 相似文献
8.
李刚常 《应用数学和力学(英文版)》1998,19(2):135-146
I.IntroductionSinceE.T.Whittaker.proposedfoestabilit}'problellll'lofnonholononlicsystemsin1904forthefirsttime,thescholarsathomeandabroad11a\'emadealotofresearchesontheequilibriunlstabilityoflinearand11olllinearnonllolollolnicsystems,andhaveobtainedaseriesofimportantresultslZ--7].Hobbled'er,theexpositionandapplicationrelatedtoLagrange'stheorenlinthestabilityanalysisfornonholonomicsystemsisseldonlseenuptonow.Althoughitwasmentionedinreference[3].aspecialdiscussionhasnotbeencarriedoutyet.Asafam… 相似文献
9.
Antony A. Hill 《Continuum Mechanics and Thermodynamics》2006,18(3-4):253-258
Linearised instability and nonlinear stability bounds for thermal convection in a fluid-filled porous finite box are derived. A nonuniform temperature field in the steady state is generated by maintaining the vertical walls at different temperatures. The linearised instability threshold is shown to be well above the global stability boundary, which is strongly suggested by the lack of symmetry in the perturbed system. The numerical results are evaluated utilising a newly developed Legendre-polynomial-based spectral method. 相似文献
10.
Z. Kwang-Hua Chu 《Mechanics Research Communications》2003,30(6):623-628
The stability problem related to the basic flows induced by the peristaltic waves propagating along the deformable walls is investigated numerically. The neutral stability boundary is obtained by solving the relevant Orr–Sommerfeld equation via a verified preconditioned complex-matrix solver. The critical Reynolds number becomes 577.25 when the ratio of the wave speed to the maximum speed of the basic flow (c/umax) becomes 10. 相似文献
11.
The aim of this paper is to present and compare two different approaches for aeroelastic stability analysis of a flexible over-expanded rocket nozzle. The first approach is based on the aeroelastic stability models developed in a previous work, while the second uses the numerical fluid–structure coupling via the transpiration method. The aeroelastic frequencies of the nozzle obtained by various stability models are compared with those extracted from the numerical coupling by the method of transpiration. Both set of results show an overall good agreement. 相似文献
12.
Global dynamical behavior of a three-body system with flexible connection in the gravitational field
Summary In this paper, the global behavior of relative equilibrium states of a three-body satellite with flexible connection under
the action of the gravitational torque is studied. With geometric method, the conditions of existence of nontrivial solutions
to the relative equilibrium equations are determined. By using reduction method and singularity theory, the conditions of
occurrence of bifurcation from trivial solutions are derived, which agree with the existence conditions of nontrivial solutions,
and the bifurcation is proved to be pitchfork-bifurcation. The Liapunov stability of each equilibrium state is considered,
and a stability diagram in terms of system parameters is presented.
Received 10 March 1998; accepted for publication 21 July 1998 相似文献
13.
V. D. Potapov 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(11):883-894
An efficient method to investigate the stability of elastic systems subjected to the parametric force in the form of a random
stationary colored noise is suggested. The method is based on the simulation of stochastic processes, numerical solution of
differential equations, describing the perturbed motion of the system, and the calculation of top Liapunov exponents. The
method results in the estimation of the almost sure stability and the stability with respect to statistical moments of different
orders. Since the closed system of equations for moments of desired quantities y
j
(t) cannot be obtained, the statistical data processing is applied. The estimation of moments at the instant t
n
is obtained by statistical average of derived from the solution of equations for the large number of realizations. This approach allows us to evaluate the influence
of different characteristics of random stationary loads on top Liapunov exponents and on the stability of system. The important
point is that results found for filtered processes, are principally different from those corresponding to stochastic processes
in the form of Gaussian white noises. 相似文献
14.
A. V. Proskurin A. M. Sagalakov 《Journal of Applied Mechanics and Technical Physics》2008,49(3):383-390
The stability of the plane flow of an electrically conducting fluid with respect to small perturbations was studied at large
Reynolds numbers in the presence of a longitudinal magnetic field. The dependence of the critical Reynolds number on the electrical
conductivity is investigated. At large Reynolds numbers, a new branch of instability and a sudden change in the critical Reynolds
numbers is found.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 45–53, May–June, 2008. 相似文献
15.
Ameer Hassan 《Nonlinear dynamics》1996,10(2):105-133
Periodic response of nonlinear oscillators is usually determined by approximate methods. In the "steady state" type methods, first an approximate solution for the steady state periodic response is determined, and then the local stability of this solution is determined by analyzing the equation of motion linearized about this predicted "solution". An exact stability analysis of this linear variational equation can provide erroneous stability type information about the approximate solutions. It is shown that a consistent stability type information about these solutions can be obtained only when the linearized variational equation is analyzed by approximate methods, and the level of accuracy of this analysis is consistent with that of the approximate solutions. It is demonstrated that these consistent stability results do not imply that the approximate solution is qualitatively correct. It is also shown that the difference between an approximate and the next higher order stability analysis can be used to "guess" the role of higher harmonics in the periodic response. This trial and error procedure can be used to ensure the qualitatively correct and numerically accurate nature of the approximate solutions and the corresponding stability analysis. 相似文献
16.
This paper presents a stability analysis of an oscillating body subjected to fluid forces located in a transient incompressible viscous flow. If the body is supported by elastic springs, oscillation will begin. If the characteristic period of the body and the excited oscillating period due to fluid forces match each other, resonance can occur. Stability analysis is therefore needed to determine the nonlinear behavior of the body. This paper presents an analysis of the changing stability of bodies by the numerical computation. To implement the computation, the motion of fluid around a body is expressed by the Navier–Stokes equation described in the arbitrary Lagrangian–Eulerian form. The fluid influence on the body is discretized by the finite element method based on a mixed interpolation by the bubble function in space. The motion of the body is assumed to be expressed by the equations of motion. To evaluate stability, stability function is defined by the total energy of the oscillating body. The stability is judged according to a stability index, obtained by the use of the automatic differentiation (AD) of the stability function. AD is a derivative computation method that gives high accuracy. By the use of AD, the second‐order derivative matrix, which is needed to compute the stability index, can be obtained exactly. For the numerical studies, analyses of one degree of freedom and two degrees of freedom (2DOF) for a circular cylinder and 2DOF for a rectangular cylinder are carried out. A combination of a cylinder and supporting elastic spring can produce stable, neutral and unstable states. It is shown that the stability of the cylinder can be determined by the stability index. This paper shows new possibilities for stability analysis of bodies located in a fluid flow. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
应用判别差分方程稳定性的Schur-Cohn准则,研究用于一般耦合系统动力响应分析的单步Newmark预测-校正算法的稳定性问题;给出了算法无条件稳定的充分必要条件的严格理论证明。 相似文献
18.
An airfoil with a cavity traps a vortex; the lift increases but the vortex shows great receptivity to upstream disturbances.
A simple potential flow model confirms that the vortex stability basin is of a reduced extent. In this paper we present a
control technique stabilizing the vortex position based on a potential flow model. The actuators are sources/sinks at the
wall and the suction/blowing law is obtained by the adjoint optimization method.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
19.
Xiong Aokui 《Acta Mechanica Sinica》2002,18(6):603-607
Based on the stability analysis with no linearization and expansion, it is argued that instability in the lattice BGK model
is originated from the linear relaxation hypothesis of collision in the model. The hypothesis stands up only when the deviation
from the local equilibrium is weak. In this case the computation is absolutely stable for real fluids. But for flows of high
Reynolds number, this hypothesis is violated and then instability takes place physically. By performing a transformation a
quantified stability criteria is put forward without those approximation. From the criteria a sufficient condition for stability
can be obtained and serve as an estimation of the limited Reynolds number as high as possible. 相似文献
20.
The influence of design characteristics (elastic characteristics of tires and asymmetry of cornering forces) on the stability and handling of a vehicle is studied. The parameter continuation method is used to validate the results of constructing bifurcation sets in the space of two control parameters.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 136–143, November 2004.This revised version was published online in April 2005 with a corrected cover date. 相似文献