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1.
For a generalized Hamiltonian system, stability for the manifolds of equilibrium states is presented based on Lyapunov’s stability
theories. Equilibrium equations, perturbation equations and first approximate equations of the system are given. A theorem
for the stability of manifolds of equilibrium states of general autonomous system is used to the generalized Hamiltonian system,
and three propositions on the stability of manifolds of equilibrium states of the system are obtained. Two examples are given
to illustrate application of the method and results. 相似文献
2.
S. V. Babenko 《International Applied Mechanics》2011,47(1):86-96
Linear systems of dynamic equations with periodic coefficients and structural perturbations on time scale are analyzed for
Lyapunov stability. Sufficient conditions for the asymptotic stability of the equations are established based on the matrix-value
concept of Lyapunov’s direct method for all values of the structural matrix from the structural set. A system of two dynamic
equations on time scale is considered as an example of applying the theoretical results obtained 相似文献
3.
The stability problem of two-dimensional compressible flat-plate boundary layers is handled using the linear stability theory.
The stability equations obtained from three-dimensional compressible Navier–Stokes equations are solved simultaneously with
two-dimensional mean flow equations, using an efficient shoot-search technique for adiabatic wall condition. In the analysis,
a wide range of Mach numbers extending well into the hypersonic range are considered for the mean flow, whereas both two-
and three-dimensional disturbances are taken into account for the perturbation flow. All fluid properties, including the Prandtl
number, are taken as temperature-dependent. The results of the analysis ascertain the presence of the second mode of instability
(Mack mode), in addition to the first mode related to the Tollmien–Schlichting mode present in incompressible flows. The effect
of reference temperature on stability characteristics is also studied. The results of the analysis reveal that the stability
characteristics remain almost unchanged for the most unstable wave direction for Mach numbers above 4.0. The obtained results
are compared with existing numerical and experimental data in the literature, yielding encouraging agreement both qualitatively
and quantitatively.
相似文献
4.
Guo-Dong Lei · Yu-Xin Ren Department of Engineering Mechanics Tsinghua University Beijing China 《Acta Mechanica Sinica》2011,27(2):179-188
The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is ex- tended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agree- ment with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows. 相似文献
5.
Stability for manifolds of equilibrium state of generalized Hamiltonian system with additional terms
For a generalized Hamiltonian system with additional terms, stability for the manifolds of the equilibrium state is presented. Equilibrium equations, disturbance equations and the first approximate equations of the system are given. A theorem for the stability of the manifolds of the equilibrium state of a general autonomous system is used for the generalized Hamiltonian systems with additional terms, and three propositions on the stability of the manifolds of the equilibrium state of the system are obtained. An example is given to illustrate the application of the method and results. At last, we study the stability for manifolds of the equilibrium state of the Euler equations of a rigid body subjected to external moments of force, by using of the method in this paper. 相似文献
6.
We consider non-linear viscous shallow water models with varying topography, extra friction terms and capillary effects, in
a two-dimensional framework. Water-depth dependent laminar and turbulent friction coefficients issued from an asymptotic analysis
of the three-dimensional free-surface Navier–Stokes equations are considered here. A new proof of stability for global weak
solutions is given in periodic domain Ω = T2, adapting the method introduced by J. Simon in [15] for the non-homogeneous Navier–Stokes equations. Existence results for
such solutions can be obtained from this stability analysis. 相似文献
7.
8.
舒煌 《应用数学和力学(英文版)》1990,11(8):779-785
On the stability analysis of large-scale systems by Lyapunov functions, it is necessary to determine the stability of vector comparison equations. For discrete systems, only the stability of linear autonomous comparison equations was studied in the past. In this paper, various criteria of stability for discrete nonlinear autonomous comparison equations are completely established. Among them, a criterion for asymptotic stability is not only sufficient, but also necessary, from which a criterion on the function class C
1
is derived. Both of them can be used to determine the unexponential stability, even in the large, for discrete nonlinear (autonomous or nonautonomous) systems. All the criteria are of simple algebraic forms and can be readily used.Projects Supported by the National Natural Science Foundation of China, 1880359. 相似文献
9.
Alessandra Lunardi 《Archive for Rational Mechanics and Analysis》1995,130(1):1-24
We study the stability of the null solution of a class of nonlinear evolution equations in Banach space. After stating a local existence result and the principle of linearized stability, we study the critical case, giving sufficient conditions for stability. The results are applied to second-order fully nonlinear parabolic equations in [0, + [ × R
n
. 相似文献
10.
11.
A finite volume turbulence model for the resolution of the two‐dimensional shallow water equations with turbulent term is presented. After making a finite volume discretization of the depth‐averaged k–ε equations in conservative form, the q–r equations, that give stability to the process, are obtained. Wall and inlet boundary conditions for the turbulent equations and wall conditions for the hydrodynamic equations are discussed. A comparison between the k–ε and q–r models and some experimental results is made. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
12.
This paper deals with dynamic stability of a viscoelastic rotating shaft subjected to a parametric random axial compressive thrust, by using moment Lyapunov exponents and the largest Lyapunov exponents as indicators. The equation of motion for the shaft is derived, which is a system of gyroscopic stochastic differential equations. The method of stochastic averaging is used to decouple the governing equations into Itô equations, from which the moment Lyapunov exponent is obtained by using mathematical transformations only. The largest Lyapunov exponent is obtained through its relation with moment Lyapunov exponents. The effects of various parameters on the stochastic dynamic stability are discussed. The approximate analytical results are confirmed by Monte Carlo simulation. 相似文献
13.
The paper presents single-term Haar wavelet series (STHWS) approach to the solution of nonlinear stiff differential equations
arising in nonlinear dynamics. The properties of STHWS are given. The method of implementation is discussed. Numerical solutions
of some model equations are investigated for their stiffness and stability and solutions are obtained to demonstrate the suitability
and applicability of the method. The results in the form of block-pulse and discrete solutions are given for typical nonlinear
stiff systems. As compared with the TR BDF2 method of Shampine and Gill’s method, the STHWS turns out to be more effective
in its ability to solve systems ranging from mildly to highly stiff equations and is free from stability constraints. 相似文献
14.
15.
This paper deals with the linear stability of a liquid film flowing down an inclined plane. The Navier-Stokes equations were reduced into four evolution equations that describe the development of the film depth, the flow rate, the free surface velocity, and the wall shear stress, using the Karman-Polhausen boundary layer integral method. Thus, we were able to determine the stability threshold and approach well the critical wave number for long waves. The obtained results were found to be in good agreement with the experiments of Liu et al. 相似文献
16.
This study analyzes the stability of an initially sharp interface between two miscible fluids in a porous medium. Linear stability equations are first derived using the similarity variable of the basic state, and then transformed into a system of ordinary differential equations using a spectral expansion with and without quasi-steady-state approximation (QSSA). These transformed equations are solved using the eigenanalysis and initial value problem approach. The initial growth rate analysis shows that initially the system is unconditionally stable. The stability characteristics obtained under the present QSSA are quantitatively same as those obtained without the QSSA. To support these theoretical results, numerical simulations are conducted using the Fourier-spectral method. The results of theoretical linear stability analyses and the numerical simulations validate to each other. 相似文献
17.
Yunfei Lv Rong Yuan Yongzhen Pei Tongtong Li 《Journal of Dynamics and Differential Equations》2017,29(2):501-521
This article deals with a stage-structured model with state-dependent delay which is assumed to be an increasing function of the population density with lower and upper bound. Firstly, according to the principle of linearized stability (Theorem 3.6, Hartung et al. in Handbook of differential equations: ordinary differential equations, 2006), we study the local stability of system in combination with the positivity and boundedness of solutions. By using the comparison principle obtained and an iterative method, the global stability of the equilibria is completely analyzed. Our results show how the interaction between interspecific and intraspecific competition affects the coexistence of both species. 相似文献
18.
Building on Evans-function techniques developed to study the stability of viscous shocks, we examine the stability of strong-detonation-wave solutions of the Navier-Stokes equations for reacting gas. The primary result, following [1, 17], is the calculation of a stability index whose sign determines a necessary condition for spectral stability. We show that for an ideal gas this index can be evaluated in the Zeldovich-von Neumann-Döring limit of vanishing dissipative effects. Moreover, when the heat of reaction is sufficiently small, we prove that strong detonations are spectrally stable provided that the underlying shock is stable. Finally, for completeness, we include the calculation of the stability index for a viscous shock solution of the Navier-Stokes equations for a nonreacting gas. 相似文献
19.
The loss of the stability of the trivial downhanging equilibrium position of a slender circular tube conveying incompressible fluid flow is studied. The tube is clamped at its upper end and is free at its lower end. Inbetween, the three-dimensional transversal motion is constrained by an elastic support considered to be rotationally symmetric. Tube equations valid for large displacement but small strain based on Kirchhoff's rod theory and the Kelvin-Voigt viscoelastic law are used.The stability analysis is performed by making use of the methods of the equivariant bifurcation theory; that is, but using the symmetry properties of the original system to drrive the amplitude equations of the critical modes. Two different types of results are given: First, for the perfect O(2)-symmetric system all three generic coincident eigenvalue cases of loss of stability in two-parameter families. Second, for the system with broken O(2)-symmetry due to imperfections, three special cases of loss of stability at simple eigenvalues. 相似文献
20.
For a fractional generalized Hamiltonian system, in terms of Riesz derivatives, stability theory for the manifolds of equilibrium states is presented. The gradient representation and second order gradient representation of a fractional generalized Hamiltonian system are studied, and the conditions under which the system can be considered as a gradient system and a second order gradient system are given, respectively. Then, equilibrium equations, disturbance equations, and first approximate equations of a fractional generalized Hamiltonian system are obtained. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to a fractional generalized Hamiltonian system, and three propositions on the stability of the manifolds of equilibrium states of the system are investigated. As the special cases of this article, the conditions which a fractional generalized Hamiltonian system can be reduced to a generalized Hamiltonian system, a fractional Hamiltonian system and a Hamiltonian system are given, respectively, and the stability theory for the manifolds of equilibrium states of these systems are obtained. Further, a fractional dynamical system and a fractional Volterra model of the three species groups are given to illustrate the method and results of the application. Finally, by using the method in this paper, we construct a new kind of fractional dynamical model, i.e. the fractional Hénon–Heiles model, and we study its stability of the manifolds of equilibrium states. 相似文献