Abstract
High-amplitude response suppression of the primary resonance of a nonlinear plant under cubic velocity feedback control is investigated. By means of the multiple scales method, two equations on the amplitude and phase of the response of the nonlinear system are obtained and the force-response and frequency-response curves are shown. The stability analyses for the open- and closed-loop responses of the system are carried out and the performance of the control strategy is investigated. The instantaneous power requirement of the control law is also examined. It can be demonstrated that appropriate choice for the feedback gain can greatly reduce the response amplitude of the primary resonance and completely eliminate the multiple responses. Finally the perturbation solutions are verified with numerical simulations.
Highlights
With the advances in design methods and structural materials, modern systems need to face higher disturbances with lower damping and increased compliance, resulting in larger and often nonlinear vibrations
The purpose of this paper is to present a feasible methodology that can achieve good control performance for a nonlinear dynamic system subjected to a primary resonance excitation
A nonlinear control law based on cubic velocity feedback is introduced to suppress the large-amplitude vibration of a thin, uniform cantilever beam subjected to a primary resonance excitation
Summary
With the advances in design methods and structural materials, modern systems need to face higher disturbances with lower damping and increased compliance, resulting in larger and often nonlinear vibrations. Analytical and experimental results have indicated that the nonlinear systems, when subjected to dynamic loads, may display a wealth of phenomena including subharmonic and superharmonic oscillations, period multiplying bifurcations, co-existing small and large amplitude oscillations in resonant regions, limit cycles, chaotic vibrations, and dynamic jumps [1,2] These typical nonlinear behaviors may cause unacceptable vibrations and are often dangerous and undesirable. El-Badawy and Nayfeh [10] used two control laws based on linear velocity feedback and cubic velocity feedback to suppress the high-amplitude vibrations of a structural dynamic model of the twin-tail assembly of an F-15 fighter when subjected to primary resonance excitations. A more general nonlinear single-degree-of-freedom system is considered, which includes velocity-dependent damping forces, polynomial and differential-polynomial nonlinearities This model is capable of describing with a reasonable degree of accuracy the nonlinear behaviors of the systems in many engineering applications. The numerical simulations of the nonlinear plant are performed to confirm and validate the perturbation solutions
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