Direct and parametric excitation of a nonlinear cantilever beam of varying orientation with time-delay state feedback

2009 ◽  
Vol 324 (3-5) ◽  
pp. 892-902 ◽  
Author(s):  
Mustafa Yaman
Keyword(s):  
Time Delay ◽  
Cantilever Beam ◽  
Parametric Excitation ◽  
State Feedback

scholarly journals The Vibration reduction of a cantilever beam subjected to parametric excitation using time delay feedback

2017 ◽  
Vol 13 (2) ◽  
pp. 7186-7193
Author(s):  
Y A Amer
Keyword(s):  
Time Delay ◽  
Cantilever Beam ◽  
Parametric Excitation ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Multiple Scale ◽  
Steady State Solution ◽  
State Feedback Control ◽  
Resonance Case

In this paper, dynamical behavior of a cantilever beam subject to parametric excitation under state feedback control with time delay is analyzed. The method of multiple scale perturbation technique is applied to obtain the solution up to the first order approximation. We obtain equations for the amplitude and phase. We studied all resonance cases numerically. Stability of the steady state solution for the selected resonance case is studied applying Rung-Kutta fourth method and frequency response equation via Matlab 7.0 and maple 16. From the results, it can be seen that the frequency and amplitude responses for the selected resonance case can be affected by the time delayed control. Effects of different parameters of the system are studied.

Vibration Control of a Cantilever Beam with Time Delay State Feedback

2006 ◽  
Vol 61 (12) ◽  
pp. 629-640 ◽  
Author(s):  
Atef F. El-Bassiouny
Keyword(s):  
Time Delay ◽  
Vibration Control ◽  
Cantilever Beam ◽  
State Feedback ◽  
Multiple Scales ◽  
State Feedback Control ◽  
Response Curves ◽  
Flow Equations ◽  
Equivalent Damping ◽  
The Stability

The primary and subharmonic resonance of order one-third of a cantilever beam under state feedback control with a time delay are investigated. Using the method of multiple scales, we obtain two slow flow equations for the amplitude and phase. The first-order approximate solution is derived and the effect of time delay on the resonance is investigated. The concept of an equivalent damping, related to the delay feedback, is proposed and an appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. The fixed points corresponding to the periodic motion of the starting system are determined, and the frequency-response and external excitation-response curves are shown. Bifurcation analysis is conducted in order to examine the stability of the system.

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