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1.
Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity-it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity.The Poincaré map,describing evolution from an impact to the next impact,is derived and scenarios of transition to chaotic dynamics are investigated analytically and numerically. 相似文献
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The to and fro motion of a bouncing ball on a flat surface is represented by a low-dimensional model. To describe the repeated reversals of the horizontal velocity of the ball, the elasticity of the ball has to be taken into account. We show that a simple fly-wheel model exhibits the observed hither and thither motion of elastic balls. The suggested model is capable of describing oblique impacts of spherical bodies, which can be important in many applications, including dynamical simulation of granular materials. We find that the behaviour of the bouncing fly-wheel is sensitive to the initial conditions, and the escape time plots are used to illustrate this observation. 相似文献
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NONLINEAR STABILITY OF BALANCED ROTOR DUE TO EFFECT OF BALL BEARING INTERNAL CLEARANCE 总被引:2,自引:0,他引:2
Stability and dynamic characteristics of a ball bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Floquet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system. 相似文献
5.
《Particuology》2017
The motion of a particle on a screen is directly affected by the motion of the screen if airflow and intergranular friction are ignored. To study this effect, a mathematical model was established to analyze the motion of a planar reciprocating vibrating screen, and a matrix method was employed to derive its equation of motion. The motion of the screen was simulated numerically and analyzed using MATLAB. The results show that the screen undergoes non-simple harmonic motion and the law of motion of each point in the screen is different. The tilt angle of the screen during screening is not constant but varies according to a specific periodic function. The results of numerical simulations were verified through experiments. A high-speed camera was used to track the motion of three points in the longitudinal direction of the screen. The balance equation for forces acting on a single particle on the screen was derived based on the non-simple harmonic motion of the screen. These forces were simulated using MATLAB. Different types of particle motion like slipping forward, moving backward, and being tossed to different parts of the screen were analyzed. A vibro-impact motion model for a particle on the non-simple harmonic vibrating screen was established based on the nonlinear law of motion of the particle. The stability of fixed points of the map is discussed. Regimes of different particle behaviors such as stable periodic motion, period-doubling bifurcation motion, Hopf bifurcation motion, and chaotic motion were obtained. With the actual law of motion of the screen and the behavior of a particle on the screen, a theoretical basis for design optimization of the screen is provided. 相似文献
6.
V. I. Slyn’ko 《International Applied Mechanics》2008,44(7):818-829
The mechanisms whereby a double pendulum with vibrating point of suspension loses stability in equilibrium positions are studied.
Stability conditions for the equilibrium positions in critical cases are established
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 120–133, July 2008. 相似文献
7.
In this paper the philosophy of mathematical phenomenological mapping has been applied to the non-linear dynamics of spur gears and radial ball bearings. The spur gear pair dynamics and rolling element bearing dynamics are analyzed separately, but with a tendency to reduce the both of the systems to the same mathematical model. The different reasonable assumptions are taken in every of these analyzes, but they do not have significant influence to the accuracy of the results. The systems are reduced to the single degree of freedom dynamics model. The total gear stiffness and ball bearing stiffness are recognized as the main influent factor of vibration behavior of these machine elements. Therefore, the special attention was paid to the new approach and procedure for stiffness solving and related problems. A single spur gear pair dynamics is solved and the results for total gear stiffness and vibration are shown. The conclusions emphasize the importance of described parallel analyzes in order to reduce the calculation time in solving different phenomena with usage of the principle of mathematical phenomenology. 相似文献
8.
By use of the LDV, experimental investigation was carried out for a turbulent boundary layer which was disturbed with an electric-magnetic
vibrating ribbon. It is found that, in the flow, the response of the disturbance contains harmonic components besides the
fundamental frequency of the ribbon vibration. The fundamental and harmonic disturbances can also enhance the energy of other
frequency components around them. In the experiments, the regular disturbane was introduced in the outer region of the boundary
layer. Under the given flow conditions, they can significantly influence the downstream coherent structures in the wall region
by suppressing the bursts and increasing their period. The effect on the burst period depends on the disturbing frequency.
The project supported by the National Natural Science Foundation of China 相似文献
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This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid,
clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or
the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin
method. The static stability is studied by the Routh criteria. The method of averaging is employed to examine the analytical
results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability
by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one
makes the periodic motions of the system lose the stability by doubling-period bifurcation.
The project supported by the Science Foundation of Tongji University and Tongji University and National Key Projects of China
under Grant No. PD9521907. 相似文献
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The stability and bifurcation of the trivial solution in the two-dimensional differential equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifurcating periodic solution and the directionof Hopf bifurcation were exhibited by applying the normal form theory and the center manifold theorem.Furthermore, numerical simulation was carried out. 相似文献
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Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass,a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra,and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed.The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity. 相似文献
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A closed-form system of dynamic equations describing the free motion of a material system with variable mass–inertia characteristics is derived. The system consists of a carrying body and carried bodies (freight) and undergoes translational–rotational motion in space. The differential equations of motion derived include time-dependent parameters and allow for the inertia and varying mass of the system, etc. It is pointed out that special cases can be derived from the general equations to study various modes of motion and stability phenomena 相似文献
17.
In this paper, a modified Jeffcott model is proposed and studied in order to shed light into the dynamics of a complex system,
the Short Electrodynamic Tether (SET), which is similar to an unbalanced rotor. Due to the internal damping, a geometrically
linear SET model appears to be unstable as predicted by the linear rotordynamics theory. Some studies in the field of rotordynamics
suggest that this instability caused by internal damping do not appear if geometric nonlinearities are taken into account
in the system equations of motion. Stability and bifurcation analysis have been carried out on the modified Jeffcott model,
which accounts for geometric nonlinearities, orthotropy in the shaft's cross section, and a viscous damping-based internal
damping model. The stability results analytically obtained have been compared with a nonlinear multibody model by means of
time simulations and good agreement has been found. 相似文献
18.
M. Adda-Bedia 《Journal of the mechanics and physics of solids》2005,53(1):227-248
The dynamic propagation of a bifurcated crack under arbitrary loading is studied. Under plane loading configurations, it is shown that the model problem of the determination of the dynamic stress intensity factors after branching is similar to the anti-plane crack branching problem. By analogy with the exact results of the mode III case, the energy release rate immediately after branching under plane situations is expected to be maximized when the branches start to propagate quasi-statically. Therefore, the branching of a single propagating crack under mode I loading should be energetically possible when its speed exceeds a threshold value. The critical velocity for branching of the initial single crack depends only weakly on the criterion applied for selecting the paths followed by the branches. However, the principle of local symmetry imposes a branching angle which is larger than the one given by the maximum energy release rate criterion. Finally, it is shown that an increasing fracture energy with the velocity results in a decrease in the critical velocity at which branching is energetically possible. 相似文献
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Stability Analysis of Sliding Whirl in a Nonlinear Jeffcott Rotor with Cross-Coupling Stiffness Coefficients 总被引:13,自引:0,他引:13
An analytical study is carried out on the stability of the fullannular rub solutions of an externally excited, modified Jeffcott rotorwith a given rotor/stator clearance and cross-coupling influences. Theobtained analytical stability conditions provide an opportunity for abetter understanding of the dynamical phenomena of rotor/stator systemswith rubs, such as jump phenomena and the transition between periodicand quasi-periodic full rub responses as well as between the fullannular rubs and the partial rubs. A systematic study on the influenceof the system parameters on these phenomena is carried out. It is foundthat the simultaneous presence of the coefficient of friction and thecross-coupling stiffness coefficient with a proper value may benefit thedynamics of the rotor/stator system with rubs. 相似文献
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Qualitative study of cavitated bifurcation for a class of incompressible generalized neo-Hookean spheres 总被引:1,自引:0,他引:1
IntroductionIn 1 958,GentandLindleyobservedthephenomenonofsuddenvoidnucleationinsolidsexperimentallyintensioningahomogenousclose_grainedvulcanizedrubbercylinderforthefirsttime.ButthemathematicalmodelonvoidnucleationandgrowthhasnotbeendescribedasabifurcationproblembasedonthetheoryofnonlinearelasticmechanicsbyBall[1]until1 982 .Inrecentyears,manyinvestigationshavebeenmadeonthisaspect.Theproblemofcavitatedbifurcationforincompressibleisotropichyperelasticmaterialswithpower_lawtypehasbeeninvestig… 相似文献