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Flutter suppression of a plate-like wing via parametric excitation

机译:通过参数激励抑制板状机翼的颤动

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摘要

The present work is motivated by the well known stabilizing effect of parametric excitation of some dynamical systems such as the inverted pendulum. The possibility of suppressing wing flutter via parametric excitation along the plane of highest rigidity in the neighborhood of combination resonance is explored. The nonlinear equations of motion in the presence of incompressible fluid flow are derived using Hamilton's principle and Theodorsen's theory for modeling aerodynamic forces. In the presence of air flow, the bending and torsion modes possess nearly the same frequency. Under parametric excitation and in the absence of air flow, each mode oscillates at its own natural frequency. In the neighborhood of combination resonance, the nonlinear response is determined using the multiple scales method at the critical flutter speed and at slightly higher airflow speed. The domains of attraction and bifurcation diagrams are obtained to reveal the conditions under which the parametric excitation can provide stabilizing effect. The basins of attraction for different values of excitation amplitude reveal the stabilizing effect that takes place above a critical excitation level. Below that level, the response experiences limit cycle oscillations, cascade of period doubling, and chaos. For flow speed slightly higher than the critical flutter speed, the response experiences a train of spikes, known as 'firing,' a term that is borrowed from neuroscience, followed by 'refractory' or recovery effect, up to an excitation level above which the wing is stabilized. The results of the multiple scales method are verified using numerical simulation of the original nonlinear differential equations.
机译:当前的工作是由某些动力系统(如倒立摆)的参量激励的稳定作用所激发的。探索了在组合共振附近通过沿最高刚度平面的参量激励来抑制机翼颤动的可能性。使用汉密尔顿原理和西奥多森理论对空气动力进行建模,得出存在不可压缩流体流动时的非线性运动方程。在有气流的情况下,弯曲和扭转模式具有几乎相同的频率。在参量激励下并且在没有气流的情况下,每个模式都以其自身的固有频率振荡。在组合共振附近,使用多尺度方法在临界振颤速度和稍高的气流速度下确定非线性响应。获得了吸引图和分叉图的域,以揭示参数激发可以提供稳定作用的条件。不同激发振幅值的吸引盆显示出在临界激发水平以上发生的稳定作用。低于该水平,响应将经历极限循环振荡,周期加倍级联和混乱。对于略高于临界振颤速度的流速,响应会经历一连串的尖峰,称为“发射”,这是从神经科学中借用的术语,其后是“难熔”或恢复作用,直至达到激发水平,机翼稳定。使用原始非线性微分方程的数值模拟,验证了多尺度方法的结果。

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