Negative Velocity Feedback Control of a Nonlinear Oscillating External Panel

Document Type : Original Article

Authors

1 Mathematics Zagazig University

2 Mathematics department, Faculty of Science, Zagazig University

3 Basic sciences department, Modern Academy

Abstract

Aircraft wings, especially during flight, experience vibrations due to various forces. This research focuses on controlling these vibrations using a negative velocity feedback controller. The wing is represented as a stepped cantilever plate, acknowledging its complex shape and movement. The study considers several factors influencing wing vibrations: Axial movement: The wing's movement through the air. Smooth surfaces: Aerodynamic forces acting on the wing. Piezoelectric innervation: The use of piezoelectric materials, which can generate electrical charge in response to mechanical stress and vice-versa, for vibration control. Out-of-plane excitation: Forces acting perpendicular to the wing surface. The research uses a combination of theoretical and computational methods: Perturbation methods: Mathematical techniques to approximate solutions to complex nonlinear systems. MATLAB simulations: Computer simulations to model and analyze the wing's dynamic behavior. Routh-Hurwitz criterion: A mathematical test to determine the stability of a system. The study investigates "primary and 1:1 internal resonance condition," which refer to specific vibration modes of the wing. The goal is to determine how effectively the negative velocity feedback controller can suppress these vibrations and maintain stability. Finally, the research validates the accuracy of the methods used by comparing analytical results with numerical simulations.

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