2021
DOI: 10.1016/j.aej.2020.10.024
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Nonlinear vibrations control of a contact-mode AFM model via a time-delayed positive position feedback

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Cited by 20 publications
(8 citation statements)
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“…The very good agreement between the results achieved from various models illustrates the validity and accuracy of the proposed bond graph model [23]. When the precise mathematical model is established of gear train, the dynamic behavior of vibration characteristics and stability of the motion system can be truly grasped [24][25][26][27].…”
Section: Introductionmentioning
confidence: 55%
“…The very good agreement between the results achieved from various models illustrates the validity and accuracy of the proposed bond graph model [23]. When the precise mathematical model is established of gear train, the dynamic behavior of vibration characteristics and stability of the motion system can be truly grasped [24][25][26][27].…”
Section: Introductionmentioning
confidence: 55%
“…The resulting non-linear algebraic equations system cannot be solved analytically, leading us to adopt the Newton-Raphson numerical technique. The extracted equilibrium solutions of the amplitudes a n and phases φ n can be classified as either stable or unstable, according to Lyapunov's linearization technique [7,16,18,19,32,33,40].…”
Section: The Amplitudes and Phases Equations Of The Blade And Controllermentioning
confidence: 99%
“…Han et al [31] formulated the steady-state dynamic responses of rotating bending-torsion coupled composite Timoshenko beams subjected to distributive and/or concentrated harmonic loadings. Hamed et al [32,33] applied either time-delayed PPF or PD controllers on a multi-excitation atomic force microscopy (AFM) model in order to extract the time delay effects on the vibration control process. It is worth mentioning the importance of the homotopy perturbation method (HPM) in solving linear and non-linear problems.…”
Section: Introductionmentioning
confidence: 99%
“…The nonlinear vibrations of a contact-mode atomic force microscopy (AFM) model subjected to multi excitations are controlled via a time-delayed positive position feedback (PPF) controller by Y.S. Hamed et al [33]. To obtain the approximate nonlinear dynamical behaviour of the AFM system they applied the multiple time scales perturbation method.…”
Section: Introductionmentioning
confidence: 99%