Modeling and analyzing the active vibration control in a self-excited beam incorporating time-delayed velocity feedback

Articles in Press

Document Type : Research Paper

Authors
T. S. Amer 1
Yomna Y. Ellabban 2
Taher A. S. Bahnasy 3
1 Faculty of Science, Tanta University
2 Ain Shams University
3 Faculty of Engineering, Tanta University, Tanta 31734, Egypt
10.22055/jacm.2026.49747.6212
Abstract
This paper investigates the nonlinear dynamics and active vibration control of a self-excited structure described as a large deflection beam system. A control strategy is proposed to suppress undesired oscillations using time-delayed linear and nonlinear velocity feedback. The steady state solution and the amplitude-frequency representations are solved analytically with the Harmonic Balance Method (HBM) and validated through extensive numerical simulations, including phase-plane portraits and bifurcation diagrams (BDs). The analysis indicates that the uncontrolled system has complex dynamical behaviors like periodic, quasi-periodic and chaotic motions. The results indicate that the proposed controller is very effective in quenching self-excited vibrations. The linear gain compensates the inherent negative damping, while the nonlinear gain provides additional damping, especially effective at large amplitudes. Finally, it was shown that the loop delay can have a potential impact on the performance of vibration control. The time delay itself does not provide a destabilizing factor but introduces a structured periodic modulation of the system dynamics, which governs the transition between various oscillatory states and should be carefully considered in the design of an effective control strategy.
Keywords
Self-excited vibrations
Time-delayed control
Velocity feedback
Harmonic Balance Method
Nonlinear resonance
Subjects
Journal of Applied and Computational Mechanics

Articles in Press, Accepted Manuscript
Available Online from 11 October 2026