立方非线性机翼的二重半稳定极限环分叉
Bifurcations of 2-Multiple Semistable Limit Cycles of Airfoils with Cubic Nonlinearity
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摘要: 对定常流作用下含立方非线性刚度的二元机翼颤振系统的二重半稳环分叉以及超临界Hopf分叉和次 临界Hopf分叉进行了研究.在以线性刚度系数和流速为参数的二维参数平面内,求出了发生Hopf分叉的边界曲 线的解析解,用谐波平衡法结合流速-等效刚度-颤振振幅关系耦合图找到了发生二重半稳极限环分叉的临界流 速值.Abstract: Bifurcations of 2-multiple semi-stable limit cycles, as well as supercritical and subcritical Hopf bifurcations of an airfoil flutter system with cubic nonlinearity in incompressible flows were studied. Air speed and the linear stiffness coefficient of pitching were taken to form a 2-dimensional parameter plane, and the analytic solutions of critical boundaries of Hopf bifurcations were obtained in the 2-dimensional parameter plane. As a result, the critical speed and linear stiffness for bifurcations of the 2-multiple semi- stable limit cycles were determined by means of harmonic balance method.
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