Abstract
The purpose of this research is to conduct a preliminary investigation into the possibility of suppressing the flutter and post-flutter (chaotic) responses of a two-dimensional self-excited airfoil with a cubic nonlinear stiffness (in torsion) and linear viscous damping via closed-loop harmonic parametric excitation. It was found that the initial configuration of the proposed control scheme caused the torsional/pitch dynamics to act as a nonlinear energy sink; as a result, it was identified that the mechanisms of vibration suppression are the resonance capture cascade and the short duration or isolated resonance capture. It is the isolated resonance capture that is responsible for the second-order-like damping and full vibration suppression of the aeroelastic system. The unforced and closed-loop system was subjected to random excitation to simulate aerodynamic turbulence. It was found that the random excitation suppresses the phase-coherent chaotic response, and the closed-loop system is susceptible to random excitation.
Highlights
In this paper, a self-excited two-dimensional airfoil with a cubic nonlinear stiffness in torsion is considered
In order to better understand the results presented we must turn to the works of the UIUC Linear and Nonlinear Dynamics and Vibrations Laboratory, their work on nonlinear energy sinks (NESs)
The dynamical system under study in this work is a system of damped coupled oscillators, a main linear system that is fixed to a nonlinear attachment that acts like a nonlinear energy sink (NES)
Summary
A self-excited two-dimensional airfoil with a cubic nonlinear stiffness in torsion is considered. Ramesh and Narayanan [2] employed a control perturbation signal that consisted of an error signal with time delay multiplied by a proportional gain. They demonstrated that a simple control law could transition a chaotic aeroelastic response to stable periodic orbits. They could not completely suppress the limit cycle oscillation. Parametric excitation means that one or all of the coefficients (i.e., stiffness or damping coefficients) of the governing equations of the system are time-varying, but not necessarily harmonic. The following paragraphs will discuss some examples of quasi-periodic parametric excitation and direct harmonic periodic excitation as a means of vibration control
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