Nonlinear primary resonance in vibration control of cable-stayed beam with time delay feedback

This paper studies the nonlinear primary resonance in the vibration control of cable stayed beam with time delay feedback. Considering the continuity conditions, the in-plane nonlinear motion equations of the cable-stayed beam are obtained via the Hamilton principle. Then, utilizing the method of multiple scales, the modulation equations that govern the nonlinear dynamics of the cable-stayed beam are derived. These equations are then utilized to investigate the effect of control gain and time delay on the amplitude and frequency response behavior. Depending on the excitation amplitude and the commensurability of the delayed-response frequency to the excitation frequency, it can be demonstrated that appropriate choice for the feedback gain can greatly reduce the response amplitude of the primary resonance. Finally, numerical simulation is also given to determine the optimal value for control gain and time delays that can improve the vibrations suppression efficiency. (C) 2019 Elsevier Ltd. All rights reserved.