共查询到20条相似文献,搜索用时 15 毫秒
1.
S. Natsiavas 《Nonlinear dynamics》1995,7(3):345-363
This work investigates nonlinear dynamic response of circular rings rotating with spin speed which involves small fluctuations from a constant average value. First, Hamilton's principle is applied and the equations of motion are expressed in terms of a single time coordinate, representing the amplitude of an in-plane bending mode. For nonresonant excitation or for slowly rotating rings, a complete analysis is presented by employing phase plane methodologies. For rapidly rotating rings, periodic spin speed variations give rise to terms leading to parametric excitation. In this case, the vibrations that occur under principal parametric resonance are analyzed by applying the method of multiple scales. The resulting modulation equations possess combinations of trivial and nontrivial constant steady state solutions. The existence and stability properties of these motions are first analyzed in detail. Also, analysis of the undamped slow-flow equations provides a global picture for the possible motions of the ring. In all cases, the analytical predictions are verified and complemented by numerical results. In addition to periodic response, these results reveal the existence of unbounded as well as transient chaotic response of the rotating ring. 相似文献
2.
D.Dane Quinn 《International Journal of Non》1997,32(6):1193-1206
We study a Hamiltonian system of coupled oscillators derived from two forced pendulums, connected with a torsional spring. The uncoupled limit is described by two identical oscillators, each possessing a homoclinic orbit separating bounded from unbounded motion. We focus on intermediate energy levels which lead to detained motions, defined as trajectories that, though unbounded as t → ∞, oscillate within the region defined by the homoclinic orbit of the unperturbed system for a long but finite time. We analyze the existence and behavior of these motions in terms of equipotential surfaces. These curves provide bounds on the motion of the system and are shown to be closed for low energies. However, above some critical energy level the equipotential curves become open. The detained trajectories are shown to arise from the region of phase space that was, for appropriate energies, stochastic. These motions remain within this region for long times before finally “leaking out” of the opening in the equipotential curves and proceeding to infinity. 相似文献
3.
The response of a single-machine quasi-infinite busbar system to the simultaneous occurrence of principal parametric resonance and subharmonic resonance of order one-half is investigated. By numerical simulations we show the existence of oscillatory solutions (limit cycles), period-doubling bifurcations, chaos, and unbounded motions (loss of synchronism). The method of multiple scales is used to derive a second-order analytical solution that predicts (a) the onset of period-doubling bifurcations, which is a precursor to chaos and unbounded motions (loss of synchronism), and (b) saddle-node bifurcations, which may be precursors to loss of synchronism. 相似文献
4.
A methodology is first presented for analyzing long time response of periodically exited nonlinear oscillators. Namely, a systematic procedure is employed for determining periodic steady state response, including harmonic and superharmonic components. The stability analysis of the located periodic motions is also performed, utilizing results of Froquet theory. This methodology is then applied to a special class of two degree of freedom nonlinear oscillators, subjected to harmonic excitation. The numberical results presented in the second part of this study illustrate effects caused by the interaction of the modes as well as effects of the nonlinearities on the steady state response of these oscillators. In addition, sequences of bifurcations are analyzed for softening systems, leading to unbounded response of the model examined. Finally, the importance of higher harmonics on the response of systems with strongly nonlinear characteristics is investigated. 相似文献
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6.
提出了一种三线性滞回阻尼模型。用Krylov-Bogoliubov缓变系灵敏法研究了正弦型激励下单自由度三线性滞回系统的稳态响应。当本文的三线性模型退化为双线性模型时。本文结果与Caughey的结果是一致的。研究结果还发现。这种系统的稳态解总是稳定的,没有振幅的跳跃现象发生。但在激振力力幅达到一定值时能够发生无界响应。此外还发现,稳态振动达到峰值振幅时滞回面积(即最大滞回面积)对峰值振幅的比值和激振力力幅成正比。这个结论与双非线性滞回系统的相应结论是一致的。 相似文献
7.
IntroductionLet Yn beasequenceofi.i.d .randomvariablesonaprobabilityspace(Ω ,T ,P)andletSn =∑ni=1Yi.Bennett( 1 962 ) [1]andHoeffding ( 1 963) [2 ]respectivelystudysumsofindependentrandomvariablesandgiveimportantprobabilityinequalitiesundertheconditionwhichYi,1 ≤i≤narebound… 相似文献
8.
The potential of harvesting vibratory energy via a bistable beam subjected to subharmonic parametric excitations is investigated. The vibrating structure is a buckled beam with two stable equilibria separated by a potential barrier. The beam is subjected to a superposition of a static axial load beyond its buckling load and a harmonic axial excitation whose frequency is around twice the frequency of the buckled beam’s first vibration mode. A macro-fiber composite patch is attached to one side of the beam to convert the strain energy resulting from the beam’s oscillation into electricity. The study considers two regimes of excitations: an amplitude sweep and a frequency sweep. In the first regime, the amplitude of excitation is quasi-statically varied while the excitation frequency is tuned at twice the natural frequency of the first vibration mode. In the second regime, the excitation frequency is swept forward and backward around the subharmonic resonant frequency while the amplitude of excitation is kept constant. A theoretical model which governs the electromechanical coupling of the transverse vibrations of the beam and the output voltage is used to monitor the response as the excitation parameters are changed. An experimental setup is also built and a series of tests is performed to validate the theoretical findings. It is shown that, depending on the amplitude and frequency of excitation, the harvester can perform small-amplitude periodic intra-well motion, intra- and inter-well chaotic motions, as well as periodic inter-well motions. Experimental results also show that, as compared to the classical linear resonance, utilizing the sub-harmonic resonance of a bistable energy harvesters can result in a broadband frequency response. 相似文献
9.
The determination of periodic solutions is an essential step in the study of dynamic systems. If some of the generalized coordinates
describing the configuration of a system are angular positions relative to certain reference axes, the associated periodic
motions divide into two types: oscillatory and rotary periodic motions. For an oscillatory periodic motion, all the generalized
coordinates are periodic in time. On the other hand, for a rotary periodic motion, some angular coordinates may have unbounded
magnitude due to the persistent circulation about their pivots. In this case, although the behaviour of the system is periodic
physically, those angular coordinates are not periodic in time. Although various effective methods have been developed for
the determination of oscillatory periodic motion, the rotary periodic motion can only be determined by brute force integration.
In this paper, the incremental harmonic balance (IHB) method is modified so that rotary periodic motions can be determined
as well as oscillatory periodic motions in a unified formulation. This modified IHB method is applied to a practical device,
a rotating disk equipped with a ball-type balancer, to show its effectiveness. 相似文献
10.
The problem of parametric control of plane motions of a two-mass pendulum (swing) is considered. The swing model is a weightless rod with two lumped masses one of which is fixed on the rod and the other slides along it within bounded limits. The control is the distance from the suspension point to the moving point. The proposed control law of swing excitation and damping consists in continuously varying the pendulumsuspension length depending on the phase state. The stability of various controlled motions, including the motions near the upper and lower equilibria, is studied. The Lyapunov functions that prove the asymptotic stability and instability of the pendulum lower position in the respective cases of the pendulum damping and excitation are constructed for the proposed control law. The influence of the viscous friction forces on the pendulum stable motions and the onset of stagnation regions in the case of its excitation is analyzed. The theoretical results are confirmed by graphical representation of the numerical results. 相似文献
11.
《Journal of Fluids and Structures》2008,24(1):96-110
This paper investigates the dynamical behaviour of a fluid-conveying curved pipe subjected to motion-limiting constraints and a harmonic excitation. Based on a Newtonian method, the in-plane equation of motion of this curved pipe is derived. Then a set of discrete equations in spatial space obtained by the differential quadrature method (DQM) is solved numerically. Emphasis is placed on the possible dynamical behaviour of the curved pipe conveying fluid. The numerical results show that the pipe without motion-limiting constraints but with a harmonic force behaves as an ordinary linear system. If, however, the pipe is subjected to cubic motion-limiting constraints, nonlinear dynamic phenomena of the system will occur. Calculations of bifurcation diagrams, phase-plane portraits, time responses, power spectrum diagrams, and Poincaré maps of the oscillations clearly demonstrate the existence of chaotic and quasiperiodic motions. Moreover, it is shown that the route to chaos is via a sequence of period-doubling bifurcations. 相似文献
12.
The equations governing the response of hysteretic systems to sinusoidal forces, which are memory dependent in the classical phase space, can be given as a vector field over a suitable phase space with increased dimension. Hence, the stationary response can be studied with the aids of classical tools of nonlinear dynamics, as for example the Poincaré map. The particular system studied in the paper, based on hysteretic Masing rules, allows the reduction of the dimension of the phase space and the implementation of efficient algorithms. The paper summarises results on one degree of freedom systems and concentrates on a two degree of freedom system as the prototype of many degree of freedom systems. This system has been chosen to be in 1:3 internal resonance situation. Depending on the energy dissipation of the elements restoring force, the response may be more or less complex. The periodic response, described by frequency response curves for various levels of excitation intensity, is highly complex. The coupling produces a strong modification of the response around the first mode resonance, whereas it is negligible around the second mode. Quasi-periodic motion starts bifurcating for sufficiently high values of the excitation intensity; windows of periodic motions are embedded in the dominion of the quasi-periodic motion, as consequence of a locking frequency phenomenon. 相似文献
13.
The nonlinear behavior of a string-beam coupled system subjected to parametric excitation is investigated in this paper. Using
the method of multiple scales, a set of first order nonlinear differential equations are obtained. A numerical simulation
is carried out to verify analytic predictions and to study the steady-state response, stable solutions and chaotic motions.
The numerical results show that the system behavior includes multiple solutions, and jump phenomenon in the resonant frequency
response curves. It is also shown that chaotic motions occur and the system parameters have different effects on the nonlinear
response of the string-beam coupled system. Results are compared to previously published work. 相似文献
14.
The finite motions of a suspended elastic cable subjected to a planar harmonic excitation can be studied accurately enough through a single ordinary-differential equation with quadratic and cubic nonlinearities.The possible onset of chaotic motion for the cable in the region between the one-half subharmonic resonance condition and the primary one is analysed via numerical simulations. Chaotic charts in the parameter space of the excitation are obtained and the transition from periodic to chaotic regimes is analysed in detail by using phase-plane portraits, Poincaré maps, frequency-power spectra, Lyapunov exponents and fractal dimensions as chaotic measures. Period-doubling, sudden changes and intermittency bifurcations are observed.Part of this work was presented at the XVIIth Int. Congr. of Theor. and Appl. Mech., Grenoble, August 1988. 相似文献
15.
Periodic vibro-impacts and their stability of a dual component system 总被引:11,自引:0,他引:11
The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation
are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of
small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according
to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and
the bifurcation of periodic vibro-impacts is not smooth.
Project supported in part by National Natural Science Foundation of China under the grant 59572024 and in part by Trans-century
Training Program Foundation for the Talents by the State Education Commission of China 相似文献
16.
17.
Dynamics of a class of strongly nonlinear single degree of freedom oscillators is investigated. Their common characteristic is that they possess piecewise linear damping properties, which can be expressed in a general asymmetric form. More specifically, the damping coefficient and a constant parameter appearing in the equation of motion are functions of the velocity direction. This class of oscillators is quite general and includes other important categories of mechanical systems as special cases, like systems with Coulomb friction. First, an analysis is presented for locating directly exact periodic responses of these oscillators to harmonic excitation. Due to the presence of dry friction, these responses may involve intervals where the oscillator is stuck temporarily. Then, an appropriate stability analysis is also presented together with some quite general bifurcation results. In the second part of the work, this analysis is applied to several example systems with piecewise linear damping, in order to reveal the most important aspects of their dynamics. Initially, systems with symmetric characteristics are examined, for which the periodic response is found to be symmetric or asymmetric. Then, dynamical systems with asymmetric damping characteristics are also examined. In all cases, emphasis is placed on investigating the low forcing frequency ranges, where interesting dynamics is noticed. The analytical predictions are complemented with results obtained by proper integration of the equation of motion, which among other responses reveal the existence of quasiperiodic, chaotic and unbounded motions. 相似文献
18.
The jump and bifurcation of Duffing oscillator with hardening spring subject to narrow-band random excitation are systematically
and comprehensively examined. It is shown that, in a certain domain of the space of the oscillator and excitation parameters,
there are two types of more probable motions in the stationary response of the Duffing oscillator and jumps may occur. The
jump is a transition of the response from one more probable motion to another or vise versa. Outside the domain the stationary
response is either nearly Gaussian or like a diffused limit cycle. As the parameters change across the boundary of the domain
the qualitative behavior of the stationary response changes and it is a special kind of bifurcation. It is also shown that,
for a set of specified parameters, the statistics are unique and they are independent of initial condition. It is pointed
out that some previous results and interpretations on this problem are incorrect.
The project supported by National Natural Science Foundation of China 相似文献
19.
Finite-amplitude convective motions that arise in a two-layer system under the influence of the thermocapillary mechanism are studied. Numerical calculations have been made by the grid method for different relationships between the parameters of the fluids. A new type of instability of equilibrium is found — thermocapillary oscillations. The evolution of the oscillatory motions as the Marangoni number changes is studied. The following forms of transitions between convection regimes are established: transition from oscillatory to steady motion through an unbounded increase in the period; bifurcation of the period, accompanied by rearrangement of the three-dimensional structure of the flow. It is shown that the thermogravitational instability mechanism leads to suppression of the oscillations. 相似文献