Abstract
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.
Highlights
Over the last few years, numerous papers have been dedicated to the control of resonantly forced systems in various engineering fields
Active control of mechanical and structural vibrations is superior to passive control, because the former is more flexible in many aspects.Nayfeh and Nayfeh [1] utilized time-delay acceleration feedback to enhance stability for controlling machine-tool chatter
Qaroush and Daqaq [5] utilized a delayed feedback controller to reduce the vibrations of a macro cantilever beam and a micro cantilever sensor
Summary
Over the last few years, numerous papers have been dedicated to the control of resonantly forced systems in various engineering fields. El-Bassiouny [2,3] presented the analysis of primary and sub harmonic resonances of a cantilever beam under time-delay feedback control using averaging and multiple scales methods. Qaroush and Daqaq [5] utilized a delayed feedback controller to reduce the vibrations of a macro cantilever beam and a micro cantilever sensor. O'Malley and Kirkinis [12] with the aid of examples, illustrated the use of the RGM for singularly perturbeddifferential equations They [13] used a combined RGM-multiple scale method forsingularly perturbed problems.Yingli et al [14] studied Dynamic effects of delayed feedback control on nonlinear vibration floating raft systems. The objective of this work is to study dynamical behavior of a cantilever beam subject to parametric excitation under state feedback control with time delay. The method of multiple scale perturbation technique is applied to obtain the solutionup to the second order approximation
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