Abstract
The application of active linear absorber based on positive position feedback control strategy to suppress the high-amplitude response of a flexible beam subjected to a primary external excitation is developed and investigated. A mathematical nonlinear model that describes the single-mode dynamic behavior of the beam is considered. The perturbation method of multiple scales is employed to find the general nonlinear response of the system and four first-order differential equations governing the amplitudes and phases of the responses are derived. Then a stability analysis is conducted for the open- and closed-loop responses of the system and the performance of the control strategy is analyzed. A parametric investigation is carried out to investigate the effects of changing the damping ratio of the absorber and the value of the feedback gain as well as the effect of detuning the frequency of the absorber on the responses of the system. It is demonstrated that the positive position feedback control technique is effective in reducing the high-amplitude vibration of the model and the control scheme possesses a wide suppression bandwidth if the absorber's frequency is properly tuned. Finally, the numerical simulations are performed to validate the perturbation solutions.
Highlights
The problem of controlling the high-amplitude vibration of an externally forced beam when subjected to a principal external resonance is considered in this paper
El-Badawy and Nayfeh [2] adopted linear velocity feedback and cubic velocity feedback control laws to suppress the high-amplitude vibrations of a structural dynamic model of the twin-tail assembly of an F-15 fighter subjected to primary resonance excitations
The closed-loop high-amplitude response of the beam to a primary resonance excitation can be modeled by a nonlinear second-order differential equation, while the dynamics of the controller can be modeled by a linear second-order differential equation
Summary
The problem of controlling the high-amplitude vibration of an externally forced beam when subjected to a principal external resonance is considered in this paper. The PPF can be combined with independent modal space control [10] to design independent second-order feedback compensators for individual modes. Chen et al [21] proposed an active vibration clamping absorber technique that used a quadratic-modal-PPF strategy to design a simple second-order nonlinear controller for suppressing the vibrations of the flexible structures. A linearly designed vibration absorber may not function properly in the nonlinear region To avoid this problem, one may increase the damping because damping is proven to reduce the nonlinear effects. This work is to study the use of PPF controller in controlling the response of the high-amplitude vibration of a flexible beam subjected to a primary external excitation.
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