Analysis on the system bifurcation and coexistence of multiple solutions for typical airfoil section with freeplay

作者：Yin, Lei Lei; Zhang, Si Jin^*; Wen, Gui Lin; Xu, Hui Dong

来源：Journal of Aerospace Power, 2014, 29(6): 1410-1416.

DOI：10.13224/j.cnki.jasp.2014.06.022

• Airfoil section
• Attraction basin
• Bifurcation diagram
• Bifurcation phenomena
• Direct transition
• Freeplay
• Limit Cycle Oscillation (LCO)
• Multiple solutions

The typical airfoil section system with freeplay described by a piecewise-stiffness model was studied. The pitch angle at the maximum amplitude was chosen as the quasi-Poincare´ sections to obtain numerically the bifurcation diagram with change of flight speed. It was found the trans-critical flutter area was located on flight speed of Ma=0.71-0.75 and limit cycle oscillation area located on flight speed of Ma=0.75-0.95 based on the bifurcation diagram. The stability of limit cycle oscillation was analyzed through the constructed four-dimensional map. According to the stability and motion manifold theory, it was learnt that the attraction basin of the limit cycle oscillation was located in the interior region of limit cycle, which was validated by the numerical method at last. At the same time, the coexistence of multiple solutions and various forms of bifurcation phenomena were found in trans-critical flutter area, such as the direct transition from double periodic motion to chaos, the coexistence of multiple periodic motion and double periodic motion, and the phenomenon of jump on amplitude.

• 出版日期2014