共查询到20条相似文献,搜索用时 46 毫秒
1.
The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and frequency are investigated in detail, respectively. The results show that the universal unfolding with respect to the excitation amplitude possesses codimension 3. The transition sets in unfolding parameter plane and the bifurcation diagrams are plotted under some conditions. Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case. Some new dynamical phenomena are presented, which are the supplement of the results obtained by Sun Liang et al. 相似文献
2.
Fangqi Chen Jianshu Liang Yushu Chen Xijun Liu Hongcheng Ma 《Mechanics Research Communications》2007,34(3):213-221
The subharmonic bifurcation and universal unfolding problems are discussed for an arch structure with parametric and forced excitation in this paper. The amplitude–frequency curve and some dynamical behavior have been shown for this class of problems by Liu et al. Here, by means of singularity theory, in the case of strict 1:2 internal resonance, the bifurcation behavior of the amplitude with respect to a parameter (which is related to the amplitude of the live load imposed on the arch structures) is studied. The results indicate that it is a high codimensional bifurcation problem with codimension 5, and the universal unfolding is given. From the mechanical background, 20 forms of two parameter unfoldings with some constraints are studied. The transition sets in the parameter plane and the bifurcation diagrams are plotted. The results obtained in this paper present some new dynamic buckling patterns and abundant bifurcation phenomena. 相似文献
3.
4.
1:2 Internal Resonance of Coupled Dynamic System with Quadratic and Cubic Nonlinearities 总被引:1,自引:0,他引:1
The1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this
system in1:2 internal resonance were derived by using the direct method of normal form. In the normal forms, quadratic and cubic nonlinearities
were remained. Based on a new convenient transformation technique, the4-dimension bifurcation equations were reduced to3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding
were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior
in strong internal resonance on4-dimension center manifolds.
Paper from Chen Yu-shu, Member of Editorial Commuttee, AMM
Foundation item: the National Natural Science Foundation of China (1990510); the National Key Basic Research Special Fund (G1998020316);
the Doctoral Point Fund of Education Committee of China (D09901)
Biography: Chen Yu-shu (1931-) 相似文献
5.
On the basis of the interaction between the electromagnetic field and a solid, the imperfect sensitivity of a superconducting rod is studied in this paper. The influences of the initial deflection of the rod and the initial magnetic field on the stability are discussed. One can see that the bifurcation response of the rod with imperfections is similar to the universal unfolding of the fork bifurcation from the singularity theory.Project supported by the Foundation of the State Education Commission of China and the Natural Science Foundation of Gansu Province. 相似文献
6.
The singularity theory is applied to study the bifurcation behaviors of a reduced rotor model obtained by nonlinear transient POD method in this paper. A six degrees of freedom (DOFs) rotor model with cubically nonlinear stiffness supporting at both ends is established by the Newton's second law. The nonlinear transient POD method is used to reduce a six-DOFs model to a one-DOF one. The reduced model reserves the dynamical characteristics and occupies most POM energy of the original one. The singularity of the reduced system is analyzed, which replaces the original system. The bifurcation equation of the reduced model indicates that it is a high co-dimension bifurcation problem with co-dimension 6, and the universal unfolding (UN) is provided. The transient sets of six unfolding parameters, the bifurcation diagrams between the bifurcation parameter and the state variable are plotted. The results obtained in this paper present a new kind of method to study the UN theory of multi-DOFs rotor system. 相似文献
7.
针对磁场环境中周期外载作用下轴向运动导电条形板的非线性振动及混沌运动问题进行研究。应用改进多尺度法对横向磁场中条形板的强非线性振动问题进行求解,得到超谐波共振下系统的分岔响应方程。根据奇异性理论对非线性动力学系统的普适开折进行分析,求得含两个开折参数的转迁集及对应区域的拓扑结构分岔图。通过数值算例,分别得到以磁感应强度、轴向拉力、激励力幅值和激励频率为分岔控制参数的分岔图和最大李雅普诺夫指数图,以及反映不同运动行为区域的动力学响应图形,讨论分岔参数对系统呈现的倍周期和混沌运动的影响。结果表明,可通过相应参数的改变实现对系统复杂动力学行为的控制。 相似文献
8.
The principal resonance of a visco-elastic systems under both deterministic and random parametric excitation was investigated.
The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability
and bifurcation of steady state response were studied by means of qualitative analysis. The contributions from the visco-elastic
force to both damping and stiffness can be taken into account. The effects of damping, detuning, bandwidth, and magnitudes
of deterministic and random excitations were analyzed. The theoretical analysis is verified by numerical results.
Foundation item: the National Natural Science Foundation of China (10072049)
Biography: XU Wei (1957∼), Professor, Doctor (E-mail: weixu@nwpu.edu.cn) 相似文献
9.
Global analysis of secondary bifurcation of an elastic bar 总被引:1,自引:0,他引:1
Hu Shouxin 《Acta Mechanica Sinica》1995,11(4):327-336
In a three dimensional framework of finite deformation configurations, this paper investigates the secondary bifurcation of
a uniform, isotropic and linearly elastic bar under compression in a large range of parameters. The governing differential
equations and finite dimensional equations of this problem are discussed. It is found that, for a bar with two ends hinged,
usually many secondary bifurcation points appear on the primary branches which correspond to the maximum bending stiffness.
Results are shown on parameter charts. Secondary modes and branches are also calculated with numerical methods.
The project supported in part by the National Natural Science Foundation of China 相似文献
10.
The nonlinear response of a two-degree-of-freedom nonlinear oscillating system to parametric excitation is examined for the
case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple
scales is used to derive four first-order autonomous ordinary differential equations for the modulation of the amplitudes
and phases. The steadystate solutions of the modulated equations and their stability are investigated. The trivial solutions
lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study
the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe
type of chaos.
Project supported by the National Natural Science Foundation of China (19472046) 相似文献
11.
Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise
C
1 map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations
are not well understood. This paper considers a particular class of border-collision bifurcations, i.e., border-collision
period-doubling bifurcations. We apply a subharmonic perturbation to the bifurcation parameter, which is also known as alternate
pacing, and we investigate the response under such pacing near the original bifurcation point. The resulting behavior is characterized
quantitatively by a gain, which is the ratio of the response amplitude to the applied perturbation amplitude. The gain in
a border-collision period-doubling bifurcation has a qualitatively different dependence on parameters from that of a classical
period-doubling bifurcation. Perhaps surprisingly, the differences are more readily apparent if the gain is plotted versus
the perturbation amplitude (with the bifurcation parameter fixed) than if plotted versus the bifurcation parameter (with the
perturbation amplitude fixed). When this observation is exploited, the gain under alternate pacing provides a useful experimental
tool to identify a border-collision period-doubling bifurcation. 相似文献
12.
13.
In this paper the effect of system parametric uncertainty on the stall flutter bifurcation behavior of a pitching airfoil is studied. The aerodynamic moment on the two-dimensional rigid airfoil with nonlinear torsional stiffness is computed using the ONERA dynamic stall model. The pitch natural frequency, a cubic structural nonlinearity parameter, and the structural equilibrium angle are assumed to be uncertain. The effect on the amplitude of the response, the bifurcation of the probability distribution, and the flutter boundary is considered. It is demonstrated that the system parametric uncertainty results already in 5% probability of pitching stall flutter at a 12.5% earlier position than the point where a deterministic analysis would predict unstable behavior. Probabilistic collocation is found to be more efficient than the Galerkin polynomial chaos method and Monte Carlo simulation for modeling uncertainty in the post-bifurcation domain. 相似文献
14.
Dr. B. Wu 《Archive of Applied Mechanics (Ingenieur Archiv)》1995,65(3):133-141
Summary The influence of shear deformation on the buckling behavior of a beam supported laterally by a Winkler elastic foundation is studied. A full investigation of the bifurcation points at which, under axial load, the beam becomes critical with respect to one or two simultaneous buckling modes is made. The configurations and stabilities of the equilibrium paths that bifurcate from the critical points are derived. From the results of theoretical analysis, it becomes evident that shear deformation has a considerable effect upon the equilibriums and stabilities of the post-buckling of the beam. The results for the Bernoulli-Euler beam can be obtained as a limiting case for those of the present beam by letting the shear stiffness tend to infinity.Supported by the National Natural Science Foundation of China 相似文献
15.
In this paper, the complicated nonlinear dynamics at the equilibria of SD oscillator, which exhibits both smooth and discontinuous dynamics depending on the value of a parameter α, are investigated. It is found that SD oscillator admits codimension-two bifurcation at the trivial equilibrium when α=1. The universal unfolding for the codimension-two bifurcation is also found to be equivalent to the damped SD oscillator with nonlinear viscous damping. Based on this equivalence between the universal unfolding and the damped system, the bifurcation diagram and the corresponding codimension-two bifurcation structures near the trivial equilibrium are obtained and presented for the damped SD oscillator as the perturbation parameters vary. 相似文献
16.
Semi-analytical and semi-numerical method is used to investigate the global bifurcations and chaos in the nonlinear system
of a Van der Pol-Duffing-Mathieu oscillator. Semi-analytical and semi-numerical method means that the autonomous system, called
Van der Pol-Duffing system, is analytically studied to draw all global bifurcations diagrams in parameter space. These diagrams
are called basic bifurcation diagrams. Then fixing parameter in every space and taking parametrically excited amplitude as
a bifurcation parameter, we can observe the evolution from a basic bifurcation diagram to chaotic pattern by numerical methods.
The project supported by the National Natural Science Foundation of China 相似文献
17.
This paper summarizes the authors' research on local bifurcation theory of nonlinear systems with parametric excitation since 1986. The paper is divided into three parts. The first one is the local bifurcation problem of nonlinear systems with parametric excitation in cases of fundamental harmonic, subharmonic and superharmonic resonance. The second one is the experiment investigation of local bifurcation solutions in nonlinear systems with parametric excitation. The third one is the universal unfolding study of periodic bifurcation solutions in the nonlinear Hill system, where the influence of every physical parameter on the periodic bifurcation solution is discussed in detail and all the results may be applied to engineering. 相似文献
18.
Guihong Fan Sue Ann Campbell Gail S. K. Wolkowicz Huaiping Zhu 《Journal of Dynamics and Differential Equations》2013,25(1):193-216
In this paper, we consider a delayed system of differential equations modeling two neurons: one is excitatory, the other is inhibitory. We study the stability and bifurcations of the trivial equilibrium. Using center manifold theory for delay differential equations, we develop the universal unfolding of the system when the trivial equilibrium point has a double zero eigenvalue. In particular, we show a universal unfolding may be obtained by perturbing any two of the parameters in the system. Our study shows that the dynamics on the center manifold are characterized by a planar system whose vector field has the property of 1:2 resonance, also frequently referred as the Bogdanov–Takens bifurcation with $Z_2$ symmetry. We show that the unfolding of the singularity exhibits Hopf bifurcation, pitchfork bifurcation, homoclinic bifurcation, and fold bifurcation of limit cycles. The symmetry gives rise to a “figure-eight” homoclinic orbit. 相似文献
19.
The bifurcation and chaos of a clamped circular functionally graded plate is investigated. Considered the geometrically nonlinear
relations and the temperature-dependent properties of the materials, the nonlinear partial differential equations of FGM plate
subjected to transverse harmonic excitation and thermal load are derived. The Duffing nonlinear forced vibration equation
is deduced by using Galerkin method and a multiscale method is used to obtain the bifurcation equation. According to singularity
theory, the universal unfolding problem of the bifurcation equation is studied and the bifurcation diagrams are plotted under
some conditions for unfolding parameters. Numerical simulation of the dynamic bifurcations of the FGM plate is carried out.
The influence of the period doubling bifurcation and chaotic motion with the change of an external excitation are discussed. 相似文献
20.
A note for analysis of thermo-mechanical contact problems 总被引:2,自引:0,他引:2
A discussion about the bifurcation and non-uniqueness of solutions in the analysis of thermo-mechanical contact problems with
initial gap is given. Without loss of generality, a mechanical contact problem coupled with steady heat transfer is studied
and an example of non-uniqueness of solutions caused by the thermo-mechanical mechanism is presented. The important work is
that the non-uniqueness of solutions, which is different from that found in the analysis of the traditional frictional contact
problems, is studied in detail. The possible oscillation and non-convergence problems in the iteraction process of the numerical
computation are discussed, and an enhanced algorithm is put forward to overcome the difficulties.
Project sypported by the National Natural Science Foundation of China (Nos. 50178016, 10225212 and 19872016), the National
Key Basic Research Special Foundation (No. G1999032805) and the Foundation for University Key Teacher by the Ministry of Education. 相似文献