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1.
This paper is devoted to the analysis of the nonlinear stability of a clamped rod carrying electric current in the magnetic field which is produced by the current flowing in a pair of inifinitely long parallel rigid wires. The natural state of the rod is in the plane of the wires and is equidistant from them. Firstly under the assumption of spatial deformation, the governing equations of the problem are derived, and the linearized problem and critical currents are discussed. Secondly, it is proved that the buckled states of the rod are always in planes. Finally, the global responses of the bifurcation problem of the rod are computed numerically and the distributions of the deflections, axial forces and bending moments are obtained. The results show that the buckled states of the rod may be either supercritical or subcritical, depending on the distancz between the rod and the wires. Furthermore, it is found that there exists a limit point on the branch solution of the supercritical buckled state. This is distinctively different from the buckled state of the elastic compressive rods.Project supported by the Foundation of the Natural Science of China and Gansu Province 相似文献
2.
非圆截面弹性细杆的平衡稳定性与分岔 总被引:3,自引:1,他引:2
本文研究存在初始曲率或挠率的非圆截面弹性细杆的平衡及稳定性问题,在两端受力矩单儿作用的条件下,杆的平衡微分方程可转换为用欧拉角表述的一阶自治系统,并有可能利用相平面的奇点理论分析弹性细杆平衡状态的稳定性,文中对杆截面的对称性,以及杆的初始曲率和挠率对平衡状态性的影响进行了定性分析,导出了解析形式的稳定性判据,揭示了杆平衡状态的列态分岔现象。 相似文献
3.
载电流简支杆的磁弹性屈曲和过屈曲 总被引:3,自引:0,他引:3
讨论了磁场中载电流简支杆的非线性稳定性问题,其磁场由两根无限长平行直导线产生,并且自然状态的简支杆位于两导线的中间.结果表明,两导线间的距离和电流方向对杆过屈曲的性态有着显著的影响. 相似文献
4.
The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1∶2
internal resonance is studied in this paper. The whole parametric plane is divided into several different regions according
to the types of motions; then the distribution of steady state motions of shallow arch on the plane of physical parameters
is obtained. Combining with numerical method, the dynamics of the system in different regions, especially in the Hopf bifurcation
region, is studied in detail. The rule of the mode interaction and the route to chaos of the system is also analysed at the
end.
Project supported by National Natural Science Foundation and National Youth Science Foundation of China 相似文献
5.
The stability of a rotating, linearly elastic, extensibte rod against deflection is analysed. It is shown that the critical rotation speed is determined by the lowest eigenvalue of the linearized equations of equilibrium. The critical speed turns out to be independent of the extensibility of the rod. Load and shape imperfections change the form of the bifurcation diagram, they generate a universal unfolding of the bifurcation of the perfect rod. The numerical calculation of the deflection of the perfect rod show that the extensibility of the rod tends to increase the deflection. 相似文献
6.
Valentin B. Glavardanov Ratko B. Maretic Nenad M. Grahovac 《European Journal of Mechanics - A/Solids》2009,28(1):131-140
We consider the problem of determining the stability boundary of an elastic rod supported by Cardan joints at both ends. The rod is loaded by a compressive force and a couple. The constitutive equations of the rod take into account the compressibility of the rod axis. The stability boundary is determined by the bifurcation points of a system of eight nonlinear first order differential equations obtained by using suitable dependent variables. The type of bifurcation is examined depending on the compressibility. By numerical integration of a system of ten nonlinear first order differential equations the post-critical shape of the rod is determined. 相似文献
7.
The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C-L method. According to obtained bifurcation diagrams and combining control theory, the method of robust control of periodic bifurcation was presented, which differs from generic methods of bifurcation control. It can make the existing motion pattern into the goal motion pattern. Because the method does not make strict requirement about parametric values of the controller, it is convenient to design and make it. Numerical simulations verify validity of the method. 相似文献
8.
Dr.-Ing. P. Vielsack 《Archive of Applied Mechanics (Ingenieur Archiv)》1976,45(2):115-129
Übersicht Unter Beachtung von drei Zuständen eines Stabes mit beliebiger Form der Zeritrallinie, nämlich des spannungslosen Ausgangszustandes, des Grundverformungszustandes unmittelbar vor der Verzweigung des Gleichgewichts und des hierzu infinitesimalen Nachbarzustandes, wird eine lineare Theorie räumlicher Verzweigungsprobleme hergeleitet. Für den Fall des ideal linear elastischen Stabes werden drei Beispiele vorgeführt. Das erste ist der ursprünglich gerade Stab unter Druck und Biegung. Hier wird der Grundzustand als infinitesimal dem Ausgangszustand benachbart angenommen. Als zweites wird der ursprünglich gerade Stab unter Druck und Torsion behandelt. Hier wird ein Grundzustand mit endlichen Verformungen betrachtet. Im dritten Beispiel wird am Fall des ebenen, gebogenen Bogens mit beliebiger Achse die Vorgehensweise bei einer Vernachlässigbarkeit der Verformungen des Grundzustandes demonstriert. Insgesamt ergeben sich durchweg Aussagen, die über die der bekannten klassischen Resultate hinausgehen.
Summary Three states of a rod with arbitrary shape of the center line are considered: the initial stress-free state, the fundamental state before the bifurcation of equilibrium, and the state in an infinitesimal neighbourhood. This leads to a linear theory of stability for spatial bifurcation problems. In the case of the ideal elastic rod three examples are treated. The first one is the initially straight rod unter bending and pressure. In this case the fundamental state is considered to be infinitesimally close to the initial state. The second example is the straight rod under torsion and pressure. Here the fundamental state has finite deformations before the bifurcation. In the third example, the plane arch in bending, the deformation of the fundamental state is neglected. In all cases one gets results which are free of contradictions and more general than the classical ones.相似文献
9.
离心场中纵向悬臂梁的大范围分岔分析 总被引:2,自引:0,他引:2
采用打靶法研究了离心场中纵向悬臂梁的大范围失稳与分岔问题。分析结果证实:随着参数a(离心臂长与梁长之比)的变化,梁平衡解可能发生三种分岔现象。文中给出了平衡解的分岔形态,并发现了梁分岔解的单向跳跃现象,即突变现象。 相似文献
10.
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
11.
A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic
equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a
line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were
obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined
by using the normal form method and centre manifold theory.
Foundation item: the National Natural Science, Foundation of China (19831030)
Biography: WEI Jun-jie, Professor, Doctor, E-mail: weijj@hit.edu.cn 相似文献
12.
Codimension two bifurcation of a vibro-bounce system 总被引:1,自引:0,他引:1
A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.The project supported by the National Natural Science Foundation of China (10172042, 50475109) and the Natural Science Foundation of Gansu Province Government of China (ZS-031-A25-007-Z (key item)) 相似文献
13.
The resonances of parametric vibration with forced vibration is analyzed, the bifurcation equation of the system is obtained
and the singularity analysis is made. Some of the laws and phenomena are revealed. The transition variety and bifurcation
diagram of the physical parametric plane are given. The results can be used in engineering.
Supported by National Natural Science Foundation and Doctoral Programme Foundation of Institution of Higher Education of China. 相似文献
14.
《International Journal of Solids and Structures》2002,39(11):2987-2999
We consider the problem of determining the stability boundary for an elastic rod under thrust and torsion. The constitutive equations of the rod are such that both shear of the cross-section and compressibility of the rod axis are considered. The stability boundary is determined from the bifurcation points of a single nonlinear second order differential equation that is obtained by using the first integrals of the equilibrium equations. The type of bifurcation is determined for parameter values. It is shown that the bifurcating branch is the branch with minimal energy. Finally, by using the first integral, the solution for one specific dependent variable is expressed in terms of elliptic integrals. The solution pertaining to the complete set of equilibrium equations is obtained by numerical integration. 相似文献
15.
By virture of the singular point theory for one-dimension diffusion process and the stochastic averaging approach of energy
envelop, the bifurcation behavior of a homoclinic bifurcation system, which is in the presence of parametric white noise and
is concealed behind a codimension two bifurcation point, is investigated in this paper.
Supported by the National Science Foundation of China under Grant No. 19602016. 相似文献
16.
A class of bifurcation solutions of almost-periodic (a. p. for short) parametric vibration systems is studied by Liapunov-Schmidt
reduction. The bifurcation diagrams and formulas are given.
The Project Supported by National Natural Science Foundation of China. 相似文献
17.
The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials is examined. The
bifurcation solution for the composed sphere under a uniform radial tensile boundary dead-load is obtained. The bifurcation
curves and the stress contributions subsequent to the cavitation are given. The right and left bifurcation as well as the
catastrophe and concentration of stresses are analyzed. The stability of solutions is discussed through an energy comparison.
Project supported by the National Natural Science Foundation of China (No. 19802012). 相似文献
18.
Bifurcation and universal unfolding for a rotating shaft with unsymmetrical stiffness 总被引:1,自引:0,他引:1
The 1/2 subharmonic resonance bifurcation and universal unfolding are studied for a rotating shaft with unsymmetrical stiffness.
The bifurcation behavior of the response amplitude with respect to the detuning parameter was studied for this class of problems
by Xiao et al. Obviously, it is highly important to research the bifurcation behavior of the response amplitude with respect
to the unsymmetry of stiffness for this problem. Here, by means of the singularity theory, the bifurcation and universal unfolding
of amplitude with respect to the unsymmetrical stiffness parameter are discussed. The results indicate that it is a high codimensional
bifurcation problem with codimension 5, and the universal unfolding is given. From the mechanical background, we study four
forms of two parameter unfoldings contained in the universal unfolding. The transition sets in the parameter plane and the
bifurcation diagrams are plotted. The results obtained in this paper show rich bifurcation phenomena and provide some guidance
for the analysis and design of dynamic buckling experiments of this class of system, especially, for the choice of system
parameters.
The project supported by the National Natural Science Foundation of China (19990510), the National Key Basic Research Special
Foundation (G1998020316) and Liuhui Center for Applied Mathematics, Nankai University and Tianjin University 相似文献
19.
SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES 总被引:3,自引:0,他引:3
IntroductionAninterestingfeatureinthefreevibrationofanonlinearsystemisthefactthatthenumberofexistingnormalmodesmayexceedthenumberofdegreesoffreedom ,aphenomenonnotencounteredinalinearsystemandcausedbymodebifurcation .Thereforemuchworkhasbeendoneonthest… 相似文献
20.
A numerical analysis of flow and concentration fields of macromolecules in a, slightly curved blood vessel was carried out.
Based on these results, the effect of the bifurcation of a flow on the mass transport in a curved blood vessel was discussed.
The macromolecules turned out to be easier to deposit in the inner part of the curved blood vessel near the critical Dean
number. Once the Dean number is higher than the critical number, the bifurcation of the flow appears. This bifurcation can
prevent macromolecules from concentrating in the inner part of the curved blood vessel. This result is helpful for understanding
the possible correlations between the blood dynamics and atherosclerosis.
The project supported by National Natural Science Foundation of China (10002003), JSPS Postdoctoral Fellowship for Foreign
Researcher and Foundation for University Teachers, the Ministry of Education 相似文献