共查询到20条相似文献,搜索用时 15 毫秒
1.
Attilio Maccari 《International Journal of Non》2006,41(1):146-155
We apply a new vibration control method for time delay non-linear oscillators to the principal resonance of a parametrically excited Liénard system under state feedback control with a time delay. Using the asymptotic perturbation method, we obtain two slow flow equations on the amplitude and phase. Their fixed points correspond to limit cycles for the Liénard system. Vibration control and high-amplitude response suppression can be performed with appropriate time delay and feedback gains. Using energy considerations, we investigate existence and characteristics of limit cycles of the slow flow equations. A limit cycle corresponds to a two-period quasi-periodic modulated motion for the starting system and in order to reduce the amplitude peak of the parametric resonance and to exclude the existence of two-period quasi-periodic motion, we find the appropriate choices for the feedback gains and the time delay. 相似文献
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J.C. Ji 《International Journal of Non》2003,38(9):1387-1401
A Jeffcott rotor with an additional magnetic bearing locating at the disc is employed to investigate the effect of time delays on the non-linear dynamical behavior of the system. The time delays are presented in the proportional and derivative feedback, respectively. For the corresponding autonomous system, a linear stability analysis is performed for the system with two identical time delays in the control loop. The nature of a single Hopf bifurcation is determined by constructing a center manifold. For the non-autonomous system, the primary resonance response is studied for its small non-linear motions using the method of averaging. The effects of time delays and control gains, as well as excitation amplitude, on the amplitude of the steady-state response are investigated. Finally, experiments are carried out to validate the theoretical predictions. 相似文献
4.
Non-linear vibrations of cantilever beams with feedback delays 总被引:1,自引:0,他引:1
A comprehensive investigation of the effect of feedback delays on the non-linear vibrations of a piezoelectrically actuated cantilever beam is presented. In the first part of this work, we examine the linear and non-linear free responses of a beam subjected to a delayed-acceleration feedback. We show that the trivial solution loses stability via a Hopf bifurcation leading to limit-cycle oscillations. We analyze the stability of the dynamic response in the postbifurcation, close to the stability boundaries by examining the nature of the Hopf bifurcation and away from the stability boundaries by using the method of harmonic balance and Floquet theory. We find that, increasing the gain for certain feedback delays may culminate in quasiperiodic and chaotic oscillations of the beam.In the second part, we analyze the effect of feedback delays on a beam subjected to a harmonic base excitations. We find that the nature of the forced response is largely defined by the stability of the trivial solutions of the unforced response. For stable trivial solutions (i.e., inside the stability boundaries of the trivial solutions), the homogeneous response emanating from the feedback diminishes, leaving only the particular solution resulting from the external excitation. In this case, delayed feedback acts as a vibration absorber. On the other hand, for unstable trivial solutions, the response contains two co-existing frequencies. Depending on the excitation amplitude and the commensurability of the delayed-response frequency to the excitation frequency, the response is either periodic or quasiperiodic. 相似文献
5.
Fadi Dohnal Horst Ecker Helmut Springer 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(12):935-947
A uniform cantilever beam under the effect of a time-periodic axial force is investigated. The beam structure is discretized
by a finite-element approach. The linearised equations of motion describing the planar bending vibrations of the beam structure
lead to a system with time-periodic stiffness coefficients. The stability of the system is investigated by a numerical method
based on Floquet’s theorem and an analytical approach resulting from a first-order perturbation. It is demonstrated that the
parametrically excited beam structure exhibits enhanced damping properties, when excited near a specific parametric combination
resonance frequency. A certain level of the forcing amplitude has to be exceeded to achieve the damping effect. Upon exceeding
this value, the additional artificial damping provided to the beam is significant and works best for suppression of vibrations
of the first vibrational mode of the cantilever beam. 相似文献
6.
The traditional passive absorber is fully effective within a narrow and certain frequency band.To solve this problem,a time-delayed acceleration feedback is introduced to convert a passive absorber into an active one.Both the inherent and the intentional time delays are included.The former mainly comes from signal acquiring and processing,computing,and applying the actuation force,and its value is fixed.The latter is introduced in the controller,and its value is actively adjustable.Firstly,the mechanical model is established and the frequency response equations are obtained.The regions of stability are delineated in the plane of control parameters.Secondly,the design scheme of control parameters is performed to help select the values of the feedback gain and time delay.Thirdly,the experimental studies are conducted.Effects of both negative and positive feedback control are investigated.Experimental results show that the proper choices of control parameters may broaden the effective frequency band of vibration absorption.Moreover,the time-delayed absorber greatly suppresses the resonant response of the primary system when the passive absorber totally fails.The experimental results are in good agreement with the theoretical predictions and numerical simulations. 相似文献
7.
J. C. Ji 《Mechanics Research Communications》2003,30(3):217
The effect of time delays occurring in a proportional-integral-derivative feedback controller on the linear stability of a simple electromechanical system is investigated by analyzing the characteristic transcendental equation. It is found that the trivial fixed point of the system can lose its stability through Hopf bifurcations when the time delay crosses certain critical values. Codimension two bifurcations, which result from non-resonant and resonant Hopf–Hopf bifurcation interactions, are also found to exist in the system. 相似文献
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时滞反馈控制是一种利用时滞进行系统控制的策略,目前对该控制策略的研究多是在理论上进行探讨,少有试验研究报道. 以受简谐激励的柔性悬臂梁为对象,开展时滞反馈控制的试验研究,给出了一个多时滞控制律的设计方法. 首先给出悬臂梁系统含有时滞项的控制模态状态方程; 然后对方程进行离散化和一种特殊的状态变量增广,得到形式上不含有时滞项的标准差分方程; 最后使用离散变结构控制的方法设计控制律. 试验中采用压电片作为作动器和外界激励,应变片作为传感器,分别考虑单时滞和双时滞的情况,通过试验验证了时滞反馈控制的可行性和有效性.关键词:柔性悬臂梁;变结构控制;时滞;实验 相似文献
10.
《International Journal of Solids and Structures》2007,44(3-4):1210-1220
We investigate the problem of suppressing the vibrations of a non-linear system with a cantilever beam of varying orientation subject to parametric and direct excitation. It is known that the growth of the response is limited by non-linearity. Therefore, vibration control and high-amplitude response suppressions of the first mode of a cantilever beam can be performed using a simple non-linear feedback law. This control law is based on cubic velocity feedback. The method of multiples scales is used to construct first-order non-linear ordinary differential equations governing the modulation of the amplitudes and phases. The stability and effects of different system parameters are studied numerically. 相似文献
11.
Summary In this article, a comparative study of the control for the repetitive impacting elastic link with parametrically excited
base in rotational motion is considered. First, a sliding mode control strategy based on linearized inverse model is designed
and employed to suppress the vibrations of the elastic beam after the impact. The control concept involves the usage of an
adaptive plant inverse model as controller in feedforward configurations. Next, a linear controller is designed via Lyapunov-Floquet
transformation. In this approach, the time-periodic equations of motion are transformed into a time-invariant form, which
is suitable for the application of standard time-invariant controller-design techniques. Finally, a fuzzy logic controller
is applied for the nonlinear model of the impacting system. The momentum balance method and an empirical coefficient of restitution
is used in the collision.
Received 27 January 1999; accepted for publication 3 June 1999 相似文献
12.
Barun Pratiher 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(1):31-42
The problem of controlling the vibration of a transversely excited cantilever beam with tip mass is analyzed within the framework
of the Euler–Bernoulli beam theory. A sinusoidally varying transverse excitation is applied at the left end of the cantilever
beam, while a payload is attached to the free end of the beam. An active control of the transverse vibration based on cubic
velocity is studied. Here, cubic velocity feedback law is proposed as a devise to suppress the vibration of the system subjected
to primary and subharmonic resonance conditions. Method of multiple scales as one of the perturbation technique is used to
reduce the second-order temporal equation into a set of two first-order differential equations that govern the time variation
of the amplitude and phase of the response. Then the stability and bifurcation of the system is investigated. Frequency–response
curves are obtained numerically for primary and subharmonic resonance conditions for different values of controller gain.
The numerical results portrayed that a significant amount of vibration reduction can be obtained actively by using a suitable
value of controller gain. The response obtained using method of multiple scales is compared with those obtained by numerically
solving the temporal equation of motion and are found to be in good agreement. Numerical simulation for amplitude is also
obtained by integrating the equation of motion in the frequency range between 1 and 3. The developed results can be extensively
used to suppress the vibration of a transversely excited cantilever beam with tip mass or similar systems actively. 相似文献
13.
The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance. It is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node (SN) or Hopf bifurcation (HB) as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results. 相似文献
14.
Attilio Maccari 《Nonlinear dynamics》2008,51(1-2):111-126
Periodic solutions for parametrically excited system under state feedback control with a time delay are investigated. Using
the asymptotic perturbation method, two slow-flow equations for the amplitude and phase of the parametric resonance response
are derived. Their fixed points correspond to limit cycles (phase-locked periodic solutions) for the starting system. In the
system without control, periodic solutions (if any) exist only for fixed values of amplitude and phase and depend on the system
parameters and excitation amplitude. In many cases, the amplitudes of periodic solutions do not correspond to the technical
requirements. On the contrary, it is demonstrated that, if the vibration control terms are added, stable periodic solutions
with arbitrarily chosen amplitude and phase can be accomplished. Therefore, an effective vibration control is possible if
appropriate time delay and feedback gains are chosen. 相似文献
15.
Bifurcation Control of Parametrically Excited Duffing System by a Combined Linear-Plus-Nonlinear Feedback Control 总被引:4,自引:0,他引:4
For a parametrically excited Duffing system we propose a bifurcation control method in order to stabilize the trivial steady state in the frequency response and in order to eliminate jump in the force response, by employing a combined linear-plus-nonlinear feedback control. Because the bifurcation of the system is characterized by its modulation equations, we first determine the order of the feedback gain so that the feedback modifies the modulation equations. By theoretically analyzing the modified modulation equations, we show that the unstable region of the trivial steady state can be shifted and the nonlinear character can be changed, by means of the bifurcation control with the above feedback. The shift of the unstable region permits the stabilization of the trivial steady state in the frequency response, and the suppression of the discontinuous bifurcation due to the change of the nonlinear character allows the elimination of the jump in the quasistationary force response. Furthermore, by performing numerical simulations, and by comparing the responses of the uncontrolled system and the controlled one, we clarify that the proposed bifurcation control is available for the stabilization of the trivial steady state in the frequency response and for the reduction of the jump in the nonstationary force response. 相似文献
16.
采用多尺度法对周期变速旋转运动电流变夹层梁的动力稳定性进行了研究. 假设电流变夹层梁绕固定轴线做随时间变化的简谐周期运动,将变速度转动梁作为一个时变参激振动系统,分析了不同结构和控制参数对失稳区域的影响. 仿真结果表明,改变外加控制电场强度的大小和梁的结构参数,可改变旋转电流变夹层梁发生动力失稳的临界角速度和失稳区域. 故在一定的条件下,可以通过控制作用于电流变夹层梁的电场强度来调节旋转运动柔性梁的振动特性,提高结构的动力稳定性. 相似文献
17.
Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper. 相似文献
18.
The effects of parametric excitation on a traveling beam, both with and without an external harmonic excitation, have been studied including the non-linear terms. Non-linear, complex normal modes have been used for the response analysis. Detailed numerical results are presented to show the effects of non-linearity on the stability of the parametrically excited system. In the presence of both parametric and external harmonic excitations, the response characteristics are found to be similar to that of a Duffing oscillator. The results are sensitive to the relative strengths of and the phase difference between the two forms of excitations. 相似文献
19.
In the present paper, the delayed feedback control is applied to suppress or stabilize the vibration of the primary system
in a two degree-of-freedom dynamical system with parametrically excited pendulum. The case of a 1:2 internal resonance between
pendulum and primary system is studied. The method of multiple scales is applied to obtain second-order approximations of
the response of the system. The system stability and bifurcations of equilibrium point of the averaged equations are computed.
It is shown that the delayed feedback control can be used to suppress the vibration or stabilize the system when the saturation
control is invalid. The vibration of the primary system can be suppressed by the delayed feedback control when the original
system is in the single-mode motion. The effect of gain and delay on the vibration suppression is discussed. As the delay
varies at a fixed value of the gain, the vibration of the primary system can be suppressed at some values of the delay. The
vibration suppression performance of the system is improved at a large value of the gain. The vibration of the primary system
could be suppressed about 56% compared with the original system by choosing the appropriate values of gain and delay. The
delayed feedback control also can be used to stabilize the system when the original system is unstable. The gain and delay
could be chosen as the controlling parameters. Numerical simulation is agreement with the analytical solutions well. 相似文献
20.
D. B. Marghitu C. Diaconescu D. Boghiu 《Archive of Applied Mechanics (Ingenieur Archiv)》1998,68(3-4):259-270
Summary In this article, the control of a repetitive impacting elastic link with parametrically excited base in rotational motion
is considered. A fuzzy-logic controller is designed and employed to suppress the vibrations resulting after the impact with
an external rigid body. The momentum balance method and an empirical coefficient of restitution is used in the collision of
the two bodies. The controller is applied successfully to reduce the vibrations of the parametrically excited impacting flexible
system. Simulations for several combinations of excitation and rotation parameters are provided.
Received 21 April 1997; accepted for publication 12 September 1997 相似文献