Abstract
The time-delayed velocity and acceleration feedback control are provided to mitigate the resonances response of a nonlinear dynamic beam. By use of the method of multiple scales, the primary resonance and the 1/3 subharmonic resonance response of the controlled beam are analyzed. The excitation amplitude response peak and critical expression are obtained, and numerical simulations are also given. The effect of the feedback gains and time delayed on the steady-state response of the two types of resonances are investigated. The result show that time-delayed acceleration feedback control can effectively mitigate amplitude, and the main resonance response is affected periodically. Selecting reasonable control gain and time delay quantity can avoid the main resonance region and unstable multi-solutions, and can improve the efficiency of the vibration control.
Highlights
Beams are important structural components used in many practical engineering structures, such as gantry crane, etc
As a very important topic in structural dynamics, the moving load problem of the beam is of practical importance in engineering
The primary and 1/3 subharmonic resonance responses of a dynamics beam with moving load and time-delayed feedback is investigated in this study
Summary
Beams are important structural components used in many practical engineering structures, such as gantry crane, etc. The primary and 1/3 subharmonic resonance responses of a dynamics beam with moving load and time-delayed feedback is investigated in this study. Despite the present work being focused on the dynamical response of a structural element, the amplitude equations describing its dynamics are common to a wide variety of phenomena They naturally appear in systems involving oscillations, ranging from population [27] and climate [28] cycles in the natural environment, the oscillatory nature of waves in fluids [29], or various applications in microelectromechanical systems (MEMS) [30,31], among others. A discussion on comparing and a summary of results are presented in Sections 5 and 6
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