On the Existence of Time Delay for Rotating Beam with Proportional–Derivative Controller
Asian Research Journal of Mathematics,
A rotating beam at varying speed mathematical model is studied. Multiple time scales method is applied to the nonlinear system of differential equations and investigated the system behavior approximate solution in the instance of resonance case. We studied the system in case of applying the delayed control on the displacement and the velocity with Proportional–derivative (PD) controller. The consistency of the steady state solution in the near-resonance case is reviewed and analyzed using the Routh-Huriwitz approach. The factors on the steady state solution of the various parameters are recognized and discussed. Simulation effects are obtained using MATLAB software package. Different response curves are involved to show and compare controller effects at various system parameters.
- Non-linear dynamical system
- multiple time scales method
- active feedback controller
- time delay
How to Cite
Zhang X, Zhang D, Chen S, Hong J. Modal characteristics of a rotating flexible beam with a concentrated massbased on the absolute nodal coordinate formulation. Nonlinear Dyn. 2017;88:61–77.
Rezaei MM, Behzad M, Haddadpour H, Moradi H. Aeroelastic analysis of a rotating wind turbine blade using ageometrically exact formulation. Nonlinear Dyn. 2017;89:2367– 2392.
Arvin H, Bakhtiari-Nejad F. Non-linear modal analysis ofa rotating beam. Int. J. Non-Linear Mech. 2011;46(6):877–897.
Bekhoucha F, Rechak S, Duigou L, Cadou JM. Nonlinear forced vibrations of rotating anisotropic beams. Nonlinear Dyn. 2013;74(4):1281–1296.
Kim H, Chung J. Nonlinear modeling for dynamic analysis of a rotating cantilever beam, Nonlinear Dyn. 2016;86:1981–2002.
Latalski J. A coupled-field model of a rotating composite beam with an integrated nonlinear piezoelectric activeelement. Nonlinear Dyn. 2017;90:2145–2162.
Ali Kandil, Hany El-Gohary. Investigating the performance of a time delayed proportional derivative controller for rotating bladevibrations, Nonlinear Dyn. 2018;91:2631–2649.
Yao MH, Chen YP, Zhang W. Nonlinear vibrations of blade with varying rotating speed, Nonlinear Dyn. 2012;68:487–504.
Yao MH, Zhang W, Chen YP. Analysis on nonlinear oscillations and resonant responses of a compressor blade, Acta Mech. 2014;225:3483–3510.
Choi SC, Park JS, Kim JH. Active damping of rotating composite thin-walled beams using MFC actuators and PVDF sensors, Compos. Struct. 2006;76:362–374.
Choi SC, Park JS, Kim JH. Vibration control of pre-twisted rotating composite thin-walled beams with piezoelectricfiber composites, J. Sound Vib. 2007;300:176–196.
Joy Mondal, S Chatterjee. Controlling self-excited vibration of a nonlinear beam by nonlinear resonant velocity feedback with time-delay, International Journal of Non-Linear Mechanics 2021;131:103684.
Liang Li, Wei-Hsin Liao, Dingguo Zhang, Yongbin Guo. Dynamic modeling and analysis of rotating beams with partially covered enhanced active constrained layer damping treatment, Journal of Sound and Vibration. 2019;455:46e68.
Boumediène Chentouf, Nejib Smaoui, Exponential stabilization of a non-uniform rotating disk-beam system via a torque control and a finite memory type dynamic boundary control, Journal of the Franklin Institute. 2019;356:11318–11344.
Lyu LF, Zhu WD. Operational modal analysis of a rotating structure under ambient excitation using a tracking continuously scanning laser Doppler vibrometer system, Mechanical Systems and Signal Processing. 2021;152:107367.
Andrea Bonito, Ricardo H Nochetto, Dimitris Ntogkas, Discontinuous Galerkin approach to large bending deformation of a bilayer plate with isometry constraint, Journal of Computational Physics. 2020;423:109785. Nayfeh AH, Mook DT. Nonlinear Oscillations. Wiley, New York; 1995.
YA Amer, AT El-Sayed, Darwesh FO. Active and time delay controls on vibrations of the Micro Electro-Mechanical System (MEMS) resonator, Asian Research Journal of Mathematics. 2019;12(4):1-17. Article no.ARJOM.46389 ISSN: 2456-477X.
Robert L Borrelli, Courtney S Colman. Differential Equation, John Wiley and Sons, INC., New York; 1998.
Gradshteyn IS, Ryzhik LM. 6^th Ed. San Diego, Ca: Academic Press. 2000;1076.
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