Experimental Results on Parametric Excitation Damping of an Axially Loaded Cantilever Beam

2009 ◽  
Author(s):  
Horst Ecker ◽  
Thomas Pumho¨ssel
Keyword(s):  
Cantilever Beam ◽  
Parametric Excitation ◽  
Vibration Suppression ◽  
Excitation Frequency ◽  
Open Loop ◽  
Piezo Actuator ◽  
Combination Frequency ◽  
Bending Vibrations ◽  
Periodic Force ◽  
Parametrically Excited

In various fields of engineering, e.g. aerospace applications, robotics or the bladings of turbomachinery, slender beam-like structures are in use and subject to free bending vibrations. Since such vibrations often are not wanted because they may degrade the performance or function of the structure, it is important to have a suitable means of vibration suppression available. In this experimental study we investigate a slender cantilever beam loaded with a controlled force at its tip. The force is always oriented towards the clamping point of the beam and generated by a piezo-actuator. Force control is based on an open-loop control without feedback from the structure. To enhance vibration suppression we take advantage of the additional damping observed when a periodic force modulation at a certain frequency is applied. From several theoretical studies it is known that parametrically excited systems show increased stability, and therefore enhanced damping properties, when the parametric excitation frequency is chosen near a certain combination frequency. Due to the almost axially applied force the cantilever beam system becomes a parametrically excited system and the effect mentioned can be observed. Numerous measurement runs have been carried out and vibration suppression as a function of the excitation frequency, the excitation amplitude and the beam initial deflection has been investigated. The results are in very good agreement with theoretical predictions and for the first time the numerical and analytical results obtained earlier are confirmed by experimental work.

Active Damping of Vibrations of a Cantilever Beam by Axial Force Control

2007 ◽  
Author(s):  
Thomas Pumho¨ssel ◽  
Horst Ecker
Keyword(s):  
Cantilever Beam ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Open Loop ◽  
Active Damping ◽  
Nonlinear Feedback ◽  
Euler Beam ◽  
Bending Vibrations ◽  
Loop Control ◽  
Damping Of Vibrations

In several fields, e.g. aerospace applications, robotics or the bladings of turbomachinery, the active damping of vibrations of slender beams which are subject to free bending vibrations becomes more and more important. In this contribution a slender cantilever beam loaded with a controlled force at its tip, which always points to the clamping point of the beam, is treated. The equations of motion are obtained using the Bernoulli-Euler beam theory and d’Alemberts principle. To introduce artificial damping to the lateral vibrations of the beam, the force at the tip of the beam has to be controlled in a proper way. Two different methods are compared. One concept is the closed-loop control of the force. In this case a nonlinear feedback control law is used, based on axial velocity feedback of the tip of the beam and a state-dependent amplification. By contrast, the concept of open-loop parametric control works without any feedback of the actual vibrations of the mechanical structure. This approach applies the force as harmonic function of time with constant amplitude and frequency. Numerical results are carried out to compare and to demonstrate the effectiveness of both methods.

Suppressing Flutter Vibrations by Parametric Inertia Excitation

2009 ◽  
Vol 76 (3) ◽  
Author(s):  
Fadi Dohnal ◽  
Aleš Tondl
Keyword(s):  
Parametric Excitation ◽  
Theoretical Study ◽  
Open Loop ◽  
Elastic Instability ◽  
Excitation Mechanism ◽  
Combination Frequency ◽  
Concentrated Mass ◽  
Time Harmonic ◽  
Flow Induced Vibrations ◽  
First Time

A theoretical study of a slender engineering structure with lateral and angular deflections is investigated under the action of flow-induced vibrations. This aero-elastic instability excites and couples the system’s bending and torsion modes. Semiactive means due to open-loop parametric excitation are introduced to stabilize this self-excitation mechanism. The parametric excitation mechanism is modeled by time-harmonic variation in the concentrated mass and/or moment of inertia. The conditions for full suppression of the self-excited vibrations are determined analytically and compared with numerical results of an example system. For the first time, example systems are presented for which parametric antiresonance is established at the parametric combination frequency of the sum type.

Experimental studies on damping by parametric excitation using electromagnets

2012 ◽  
Vol 226 (8) ◽  
pp. 2015-2027 ◽  
Author(s):  
F Dohnal
Keyword(s):  
Parametric Excitation ◽  
Vibration Suppression ◽  
Experimental Studies ◽  
Mechanical Systems ◽  
Variable Stiffness ◽  
Excitation Amplitude ◽  
Open Loop ◽  
Basic Step ◽  
Mass System ◽  
Loop Control

Transient vibrations in mechanical systems are a common problem in engineering. Several theoretical studies have shown analytically and numerically that a vibrating system can be stabilised or its vibrations can be reduced when excited close to a specific parametric combination resonance frequency. At this operation, the transient vibrations are effectively damped by parametric excitation. The basic step in exploiting this method is its experimental implementation in mechanical systems. In this review, recent experiments are discussed for a simple chain mass system, a continuous cantilever and a flexible rotor system. The parametric excitation is realised by electromagnetic variable-stiffness actuators driven by a periodic open-loop control. It is demonstrated experimentally that a parametrically excited structure can exhibit enhanced damping properties. A certain level of the excitation amplitude has to be exceeded to achieve the damping effect in which the existing damping in the system is artificially amplified. Upon exceeding this value, the additional artificial damping provided to the system is significant and most effective for vibration suppression of the lower vibration modes.

Experimental Observations of Nonlinear Nonplanar Oscillations of a Cantilever Beam

2007 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh ◽  
Bashar K. Hammad
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Low Frequency ◽  
Harmonic Load ◽  
Bending Vibrations ◽  
Out Of Plane ◽  
Frequency Components ◽  
Plane Bending ◽  
The Difference

The dynamics of a thin cantilever beam undergoing combined torsion and bending vibrations are examined experimentally. The beam’s fundamental natural frequencies in the two orthogonal bending motions and in torsion are fv1 = 5.719 Hz, fw1 = 189.730 Hz, and fφ1 = 138.938 Hz, respectively. A base-excitation shaker imparts a harmonic load that acts parallel to the width of the beam. First, the response of the beam is examined when the excitation frequency is equal to the fundamental torsion natural frequency (i.e., f = 138.9 Hz). For low levels of excitation, the motion consists mainly of hardly noticeable twisting vibrations. For high levels of excitation, the energy of the first torsion mode excites the first out-of-plane bending mode. In this case, the beam responses exhibit modulated vibrations containing both high-frequency and low-frequency components. Second, the beam is excited at the frequency f = 132.0 Hz, which is in the neighborhood the difference of these two natural frequencies. For large excitation levels, the beam vibrates with large-amplitude out-of-plane bending motions that exhibit chaotically intermittent behaviors.

Bifurcation control for a parametrically excited cantilever beam by linear feedback

2012 ◽  
Vol 226 (8) ◽  
pp. 1987-1999 ◽  
Author(s):  
Hiroshi Yabuno ◽  
Masahiko Hasegawa ◽  
Manami Ohkuma
Keyword(s):  
Cantilever Beam ◽  
Control Method ◽  
Dominant Role ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Bifurcation Control ◽  
Linear Feedback ◽  
Parametrically Excited ◽  
Saddle Node ◽  
Transcritical Bifurcations

In this article, we propose a bifurcation control method for a parametrically excited cantilever beam by linear feedback. Quadratic damping plays a dominant role in the nonlinear response of the parametrically excited cantilever beam, and two transcritical bifurcations can exist in the frequency–response curve. In the relatively high-amplitude excitation or in sweeping the excitation amplitude, there are two saddle-node bifurcations in addition to the transcritical bifurcations. The discontinuous bifurcation as a saddle-node bifurcation induces jumping phenomena in the sweeps of the excitation amplitude and the excitation frequency. In this article, we focus on the case of the excitation amplitude sweep and propose a control method to avoid the jumping phenomena by bifurcation control, i.e. by shifting the bifurcation set based on the linear feedback. The validity of the control method is experimentally confirmed using a simple apparatus.

Vibration Suppression and Compliance Control of a Flexible Cantilever Beam using Manipulators

2021 ◽  
Author(s):  
Xianwei Yuan ◽  
Pengyu Jie ◽  
Yuhao Meng ◽  
Haiping Zhou ◽  
Ke Li ◽  
...  
Keyword(s):  
Cantilever Beam ◽  
Vibration Suppression ◽  
Compliance Control

Vibration suppression and energy transfer by parametric excitation in drive systems

2012 ◽  
Vol 226 (8) ◽  
pp. 2000-2014 ◽  
Author(s):  
Horst Ecker ◽  
Thomas Pumhössel
Keyword(s):  
Energy Transfer ◽  
Parametric Excitation ◽  
Vibration Suppression ◽  
Negative Impact ◽  
Energy Transfer Mechanism ◽  
Engineering Systems ◽  
Excitation Mechanism ◽  
Electrical Drive ◽  
Excitation Mechanisms ◽  
Drive Systems

Drive systems may experience torsional vibrations due to various kinds of excitation mechanisms. In many engineering systems, however, such vibrations may have a negative impact on the performance and must be avoided or reduced to an acceptable level by all means. Self-excited vibrations are especially unwanted, since they may grow rapidly and not only degrade the performance but even damage machinery. In this contribution it is suggested to employ parametric stiffness excitation to suppress self-excited vibrations. In the first part of the article we study the basic energy transfer mechanism that is initiated by parametric excitation, and some general conclusions are drawn. In the second part, a hypothetic drivetrain, consisting of an electrical motor, a drive shaft and working rolls is investigated. A self-excitation mechanism is assumed to destabilize the drive system. Parametric excitation is introduced via the speed control of the electrical drive, and the capability of stabilizing the system by this measure is investigated. It is shown that the damping available in the system can be used much more effectively if parametric stiffness excitation is employed.

scholarly journals Cantilever Beam Metastructure for Active Broadband Vibration Suppression

2020 ◽  
Author(s):  
Ratiba Fatma Ghachi ◽  
Wael Alnahhal ◽  
Osama Abdeljaber
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Vibration Suppression ◽  
Research Work ◽  
Peak Frequency ◽  
Experimental Frequency ◽  
Transmission Frequency ◽  
Vibration Attenuation ◽  
The Masses ◽  
Zigzag Structure

This paper presents a beam structure of a new metamaterial-inspired dynamic vibration attenuation system. The proposed experimental research presents a designed cantilevered zigzag structure that can have natural frequencies orders of magnitude lower than a simple cantilever of the same scale. The proposed vibration attenuation system relies on the masses places on the zigzag structure thus changing the dynamic response of the system. The zigzag plates are integrated into the host structure namely a cantilever beam with openings, forming what is referred to here as a metastructure. Experimental frequency response function results are shown comparing the response of the structure to depending on the natural frequency of the zigzag structures. Results show that the distributed inserts in the system can split the peak response of the structure into two separate peaks rendering the peak frequency a low transmission frequency. These preliminary results provide a view of the potential of research work on active-controlled structures and nonlinear insert-structure interaction for vibration attenuation.

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