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ON THE stability boundary OF HAMILTONIAN SYSTEMS

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Applied Mathematics and Mechanics(English Edition) 2002年第2期23卷 187-193页

作者：齐朝晖 Alexander P.Seyranian Department of Mcchanics Dalian University of TechnologyDalian116023P Rchina Institute of Mechanics Moscow State Lomonosov UniversityMoscow117192Russia

The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.

关键词： stability boundary Hamiltonian system sensitivity analysis perturbation method

Bifurcations and stability boundary of a Power System

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Acta Mathematicae Applicatae Sinica 2004年第3期20卷 513-532页

作者： Ying-huiGao AcademyofMathematicsandSystemsScience ChineseAcademyofSciencesBeijing100080China

A single-axis flux decay model including an excitation control model proposed in [12,14,16] is studied. As the bifurcation parameter P m (input power to the generator) varies, the system exhibits dynamics emerging from static and dynamic bifurcations which link with system collapse. We show that the equilibrium point of the system undergoes three bifurcations: one saddle-node bifurcation and two Hopf bifurcations. The state variables dominating system collapse are different for different critical points, and the excitative control may play an important role in delaying system from collapsing. Simulations are presented to illustrate the dynamical behavior associated with the power system stability and collapse. Moreover, by computing the local quadratic approximation of the 5-dimensional stable manifold at an order 5 saddle point, an analytical expression for the approximate stability boundary is worked out.

关键词： Excitation control bifurcations stability boundary system collapse

stability analysis of long hydrodynamic journal bearings based on the journal center trajectory

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Friction 2021年第6期9卷 1776-1783页

作者： Yu HUANG Haiyin CAO Zhuxin TIAN State Key Lab of Digital Manufacturing Equipment and Technology School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhan 430074China School of Mechanical Engineering Hubei University of Arts and ScienceXiangyang 441053China

In this study,we observe that there are two threshold speeds(stability threshold speed and second threshold speed)for the long journal bearing,which is different for the short bearing.When the rotating speed is below the stability threshold speed,the stability boundary nearly coincides with the clearance circle,and the journal center gradually returns to the equilibrium point after being released at an initial point.If the rotating speed is between the stability threshold speed and the second threshold speed,after being released at an initial point,the journal center converges to a contour containing the equilibrium point.In this situation,for a higher rotating speed,the corresponding contour is also larger.When the rotating speed exceeds the second threshold speed,the journal gradually moves towards the bearing surface after being released at an initial point.

关键词： long journal bearings stability threshold speed stability boundary journal center trajectory

Direct Multiscale Analysis of stability of an Axially Moving Functionally Graded Beam with Time-Dependent Velocity

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Acta Mechanica Solida Sinica 2020年第2期33卷 150-163页

作者： Ting Yan Tianzhi Yang Liqun Chen Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai 200072China Department of Mechanics Shanghai UniversityShanghai 200444China Department of Mechanics Tianjin UniversityTianjin 300072China Tianjin Key Laboratory of Nonlinear Dynamics and Control Tianjin 300072China

In this study,the transverse vibration of a traveling beam made of functionally graded material was analyzed.The material gradation was assumed to vary continuously along the thickness direction of the beam in the form of power law exponent.The effect of the longitudinally varying tension due to axial acceleration was highlighted,and the dependence of the tension on the finite support rigidity was also considered.A complex governing equation of the functionally graded beam was derived by the Hamilton principle,in which the geometric nonlinearity,material properties and axial load were incorporated.The direct multiscale method was applied to the analysis process of an axially moving functionally graded beam with timedependent velocity,and the natural frequency and solvability conditions were obtained.Based on the conditions,the stability boundaries of subharmonic resonance and combination resonance were obtained.It was found that the dynamic behavior of axial moving beams could be tuned by using the distribution law of the functional gradient parameters.

关键词： Axial motion Functionally graded beam Direct multiscale method Support rigidity stability boundary

Extreme Value Condition of Stabilizing Digital PID Region

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Extreme Value Condition of Stabilizing Digital PID Region

Sensitivity Analysis of Eigenvalues and stability Boundaries of Hamiltonian Systems

作者： Yu DONG School of Computer South China Normal University

This paper considers the stability of the digital PID control systems designed for linear time-invariant plants.The bilinear transform equation is adopted to determine the characteristic equation of the closed-loop system in the s domain.The extreme value condition of the stabilizing digital PID region is derived.Using this condition,the admissible range of the integral gain is derived.For a fixed integral gain,the stabilizing PD region is obtained by using the the stability boundary locus method.Numerical examples illustrate the method presented.

关键词： Digital PID control Stabilization stability boundary

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Sensitivity Analysis of Eigenvalues and Stability Boundaries...

The interactions and stabilty boundary of microemulsion droplets

The Fourth World Congress of Structural and Multidisciplinary Optimization

作者： Alexander P.Seyranian Institute of Mechanics Moscow State Lomonosov University Moscow117192Russia

＜正＞In this paper an approximate equation describing smooth parts of the stability boundary for linear Hamiltonian systems, depending on arbitrary number of parameters, is derived. With this equation we can get parameters corresponding to the stability boundary, as well as to stability and instability domains, when only one point on the stability boundary is known. Then differential equations describing evolution of eigenvalues and eigenvectors along a curve on the stability boundary surface are derived. These equations also allow to integrate curves belonging to the stability boundary. Applications to linear gyroscopic systems are considered and studied with examples.

关键词： stability boundary Hamiltonian systems gyroscopic systems

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The interactions and stabilty boundary of microemulsion drop...