共查询到20条相似文献,搜索用时 31 毫秒
1.
IntroductionRotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom.Synchronous vibration is its typical motion under unavoidable unbalance.Subharmonic,quasi-periodic and chaotic vibrations,caused by the … 相似文献
2.
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
3.
4.
IntroductionStabilityproblemsarisingfromengineeringapplicationsareusuallyrelatedtocertainquantitiesthatspecifythestrengthofadmissibledisturbancesandthelimitsondeviationsofmotionofthedisturbedsystem .Inthisregard ,theconventionalLiapunovstabilityconcept… 相似文献
5.
RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS
刘俊 《应用数学和力学(英文版)》2002,23(10):1229-1236
IntroductionInthesystemofnonlinearoscillating ,periodicmotionisofprimeimportance .Butexistenceofperiodicsolutionsisaverydifficultquestion .Luckilythereexistsomekindsofperiodicsolutioninactualphysicalsystems .Therefore ,weusuallyconcentratedourattentionont… 相似文献
6.
Zhu Ruzeng 《Acta Mechanica Sinica》1990,6(2):180-187
The complete solutions of the upright and oblique permanent rotations of a symmetric heavy gyroscope with perfect dissipation
are given. The asymptotic stability criteria and unstability criteria for these rotations in the sense of Liapunov and the
sense of Movchan are also given on the basis of exact nonlinear motion equations respectively. The related oblique rotations
are non-isolated. The main subdomains of the regions of asymptotic stability are obtained. The related bifurcation phenomena
are discussed in detail.
The project is supported by the National Natural Science Foundation of China. 相似文献
7.
桁架结构稳定分析的几何非线性欧拉稳定理论 总被引:3,自引:0,他引:3
目前,桁架结构稳定分析有两个理论:经典的特征值理论和几何非线性临界点理论。前者发展较早,在许多结构力学书中都有叙述。但是经过工程应用检验,它过高地估计了结构抗稳定的能力。后者是20年前提出的,提出者认为适用于所有的扁桁架。经过几年的研究,作者连续提出三个稳定理论:线性与非线性欧拉理论;非线性临界点-欧拉理论和两个计算方法,进行桁架结构的线性和非线性截面优化设计。经过理论研究和对前人文献中数值例题的计算和比较,发现特征值理论不符合实际,临界点理论只适用于大扁度的桁架,而不适用于一切扁桁架。研究结果提供了若干有用的结论,给出了各种稳定理论的适用范围,指出了国际文献中若干例题的正确和错误,补充了桁架结构的稳定分析理论,使之更为完整和实用了。 相似文献
8.
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
9.
The three-dimensional H-type nonlinear evolution process for the problem of boundary layer stability is studied by using a newly developed method called parabolic stability equations (PSE). The key initial conditions for sub-harmonic disturbances are obtained by means of the secondaryinstability theory. The initial solutions of two-dimensional harmonic waves are expressed in Landau expansions. The numerical techniques developed in this paper, including the higher order spectrum method and the more effective algebraic mapping for dealing with the problem of an infinite region, increase the numerical accuracy and the rate of convergence greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of the numerical calculation can be assured. The effects of different pressure gradients, including the favorable and adverse pressure gradients of the basic flow, on the “H-type“ evolution are studied in detail. The results of the three-dimensional nonlinear “H-type“ evolution are given accurately and show good agreement with the data of the experiment and the results of the DNS from the curves of the amplitude variation, disturbance velocity profile and the evolution of velocity. 相似文献
10.
IntroductionByadoptingtheenergymethod,anewmethodtocalculatethestabilityofthecompositeshellofrevolutionispresented.Thismethodtakestheinfluenceofnonlinearprebucklingdeformationsandstressesonthebucklingoftheshellintoaccount.Therelationshipsbetweenthepreb… 相似文献
11.
周恒 《应用数学和力学(英文版)》1991,12(3):219-225
The weakly nonlinear theory has been widely applied in the problem of hydrodynamicstability and also in other fields.However,although its application has been successful forsome problems,yet,for other problems,the results obtained are not satisfactory,especiallyfor problems like transition or the evolution of the vortex in the free shear flow,for whichthe goal of the theoretical investigation is not seeking for a steady state,but predicting anevolutional process.In this paper,we shall examine the reason for the unsuccessfulness andsuggest ways for its amendment. 相似文献
12.
Stability of dynamic equations on time scale is analyzed. The main results are new conditions of stability, uniform stability,
and uniform asymptotic stability for quasilinear and nonlinear systems
On the occasion of the 150th birthday of A. M. Lyapunov
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 3–27, September 2007. 相似文献
13.
Ramón G. Plaza 《Journal of the mechanics and physics of solids》2008,56(5):1989-2018
This paper considers phase boundaries governed by regular kinetic relations as first proposed by Abeyaratne and Knowles [1990. On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solids 38 (3), 345-360; 1991. Kinetic relations and the propagation of phase boundaries in solids. Arch. Ration. Mech. Anal. 114, 119-154]. It shows that static configurations of hyperelastic materials, in which two different martensitic (monoclinic) states meet along a planar interface, are dynamically stable towards fully three-dimensional perturbations. For that purpose, the reduced stability (or reduced Lopatinski) function associated to the static twin [Freistühler and Plaza, 2007. Normal modes and nonlinear stability behavior of dynamic phase boundaries in elastic materials. Arch. Ration. Mech. Anal. 186 (1), 1-24] is computed numerically. The results show that the interface is weakly stable under Maxwellian kinetics expressing conservation of energy across the boundary, whereas it is uniformly stable with respect to linearly dissipative kinetic rules of Abeyaratne and Knowles type. 相似文献
14.
周哲玮 《应用数学和力学(英文版)》1991,12(5):439-443
This paper discusses the nonlinear stability behaviour of distorted plane Couette flowto 2-dimensional disturbances,and compares it with that of distorted plane Poiseuille flow.The results show that plane Couette flow is more unstable than plane Poiseuille flow tofinite-amplitude disturbances. 相似文献
15.
Convection induced by the selective absorption of radiation is investigated, for the case of an internal heat source that is modelled quadratically with respect to concentration. The growth rate for the linearised system is shown to be real, and a linear instability analysis is performed. To establish conditional and unconditional nonlinear stability results, both the Darcy and Forchheimer models are employed to describe fluid flow. Due to the presence of significant regions of potential subcritical instabilities, the results indicate that linear theory may only be accurate enough to predict the onset of convective motion when the model for the internal heat source is predominantly linear.Received: 6 May 2003, Accepted: 9 August 2003, Published online: 12 December 2003 相似文献
16.
Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-dimensional (3D) mathematical model for anaiyzing the nonlinear mechanical behaviors of structures is established, in which the effects of the rotation inertia and the nonlinearity of material and geometry are considered. As an application, the nonlinear stability and the post-buckling for a linear elastic beam with the equal cross-section located on an elastic foundation are analyzed.One end of the beam is fully fixed, and the other end is partially fixed and subjected to an axial force. A new numerical technique is proposed to calculate the trivial solution,bifurcation points, and bifurcation solutions by the shooting method and the Newton-Raphson iterative method. The first and second bifurcation points and the corresponding bifurcation solutions are calculated successfully. The effects of the foundation resistances and the inertia moments on the bifurcation points are considered. 相似文献
17.
吴陈 《应用数学和力学(英文版)》1993,14(4):367-370
It is in references[4,5]that the combination of the relative researches of pansystems methodology and the researches of bifurcation,catastrophe,chaos and stability in nonlinear mechanics was put forward and the concepts were redefined from the point of view of pansystems methodology.The present paper studies the logic conservation law of these nonlinear mechanics phenomena under the framework of pansystems methodology. 相似文献
18.
IntroductionThedynamicandcontrolofcoupledrigid_flexiblesystemisaleading_edgeresearchsubjectthathasdrawnextensiveattentionfromtheacademiccommunityintheworld[1].TheresearchconductedbyKaneetal.in 1 987[2 ]suggestedthat,thetraditionalmodelapplyingstructuraldynamicsassumptionaboutelasticdeformationindiscriminately[3,4 ],ineffect,hasneglectedtheso_called“dynamicstiffening”effectresultedfromcoupledrigid_flexiblesystem .Therefore ,itisofparticularimportancetoresearchtheactionofcoupledrigid_flexibles… 相似文献
19.
Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal
disassembling technique. The effects of Poisson, Junction and Friction couplings in the wave-flowing-vibration system on the
pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing
example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling
mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable
characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points
corresponding to the various modal motions are different.
Foundation items: the National Natural Science Foundation of China (50079007); the Hydraulic Science Foundation of China Hydraulic Ministry
(SZ9830); the Natural Science Foundation of Yunnan Provicce (98E003G)
Biographies: ZHANG Li-xiang (1959−) HUANG Wen-hu (1926−) 相似文献
20.
This work is concerned with the use of new nunumerical methods to establish some new criteria to determine the equilibrium point's stability of a multidimensional nonlinear dynamic system. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献