Hopf bifurcation for a fractional van der Pol oscillator and applications to aerodynamics: implications in flutter
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Published:2023-04
Issue:1
Volume:139
Page:
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ISSN:0022-0833
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Container-title:Journal of Engineering Mathematics
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language:en
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Short-container-title:J Eng Math
Author:
Juárez Gerardo,Ramírez-Trocherie Marcel-André,Báez Ángel,Lobato Alan,Iglesias-Rodríguez Ernesto,Padilla Pablo,Rodríguez-Ramos Reinaldo
Abstract
AbstractFlutter is an important instability in aeroelasticity. In this work,we derive a model for this phenomenon which naturally leads to an equation similar to a van der Pol oscillator in which the friction term is given by a fractional derivative. Motivated by these considerations,we study a fractional van der Pol oscillator and show that it exhibits a Hopf bifurcation. The model is based on a one-dimensional reduction where the instabilities associated with flutter are preserved. However, due to the fractional derivative, the bifurcation analysis differs from the standard case. We present both analytical and numerical results and discuss the implications to aerodynamics. Additionally, we contrast our qualitative results with experimental data.
Funder
Consejo Nacional de Ciencia y Tecnología
Programa de Apoyo a la Superación del Personal Académico
Dirección General de Asuntos del Personal Académico
Publisher
Springer Science and Business Media LLC
Subject
General Engineering,General Mathematics
Reference23 articles.
1. Atanackovic TM, Pilipovic S, Stankovic B, Zorica D (2014) Fractional calculus with applications in mechanics. Wiley, Hoboken
2. Paidoussis MP (2014) Fluid–structure interactions: slender structures and axial flow, 2nd edn. Elsevier, Amsterdam
3. Theodorsen T (1935) Report No 496, general theory of aerodynamic instability and the mechanism of flutter. J Franklin Inst 219(6):766–767
4. Sewall L (1957) Experimental and theoretical study of the effect of fuel on pitching-translation flutter, 43
5. Reese R (1955) Some effects of fluid in pylon-mounted tanks on flutter, 9
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