Author:
Cheng Lifang,Liu Ming,Hu Dongpo,Zhang Litao
Abstract
AbstractBifurcations of equilibria of a wing model have been investigated in this paper. It is shown that the quintic nonlinear terms in the pitch and the plunge coordinate have affected the bifurcation structure of nontrivial equilibria in different degree. In contrast with the quintic stiffening parameter in plunge, the quintic parameter in pitch has a relatively significant effect, which will affect the number, position and stability of nontrivial equilibria. Therein two pairs of nontrivial equilibria with opposite stability coexist or disappear by two fold bifurcations. If the freestream velocity has been taken as a continuation parameter, it will affect the bifurcation structure of all the equilibria, including the trivial and the nontrivial. Wherein the equilibria vary from a trivial to two nontrivial ones by a pitchfork bifurcation. Then one of nontrivial equilibria experiences a supercritical Hopf bifurcation and the bifurcated limit cycles form an ellipsoidal structure with the limit cycles bifurcated from the trivial equilibrium.
Funder
Henan Natural Science Foundation
the Key scientifc research project of colleges and universities in Henan Province
Henan Province Key R &D and Promotion Project
the Key Scientific Research Project of Henan Higher Education Institutions
NSF of Shandong Province
China Postdoctoral Science Foundation
the Youth Creative Team Sci-Tech Program of Shandong Universities
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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