Elimination of the Flutter Phenomenon in a Forced and Self-excited Nonlinear Beam Using an Improved Saturation Controller Algorithm

Abstract

Flutter is a dynamic instability of an elastic structure subjected to fluid flow. Flutter phenomenon of the beam cannot occur unless bending and twisting vibrations occur simultaneously. This paper intends to eliminate the flutter phenomenon by suppressing the bending mode vibrations. The mathematical model under study is the Euler–Bernoulli beam reduced to the bending mode vibrations. The beam operates in the presence of external harmonic excitation on its support and fluid flow. The proposed algorithm uses the saturation controller and the velocity feedback controller together. The improved saturation controller was connected to the primary system by using a quadratic velocity coupling term, which introduces a better vibration reduction than that of the ordinary saturation controller. We applied the multiple-timescale perturbation technique (MSPT) and obtained a first-order approximate solution. We studied the effects of various controller parameters and time delays on the system response. We investigated the stability of the equilibrium solution and the time margins of various time delays and validated some analytical results numerically. Finally, we submitted further improvement to eliminate the undesired regions in the frequency response curve of the saturation controller.