In this paper, the effectiveness of nonlinear energy sinks on enhancing aeroelastic stability and post-instability response of aircraft wings is investigated. The wing has two degrees of freedom in bending and torsion, and is modelled using an extended Euler-Bernoulli beam theory with hardening nonlinearity. A Nonlinear Energy Sink (NES) absorber is embedded inside the wing distributed along the wing span. The wing attached unsteady aerodynamic loads are simulated using the Wagner's indicial lift model. The structural dynamics of the wing are derived using Extended Hamilton's Principle and it is discretised using Galerkin's method. The NES mass is connected to the wing spar through a linear damper and nonlinear spring with a cubic stiffness nonlinearity. The coupled aeroelastic equations are then transformed to state space. Then, integrated numerically to resolve the bending and torsional response of the wing to study the impact of spanwise and chordwise positions of the embedded NES on flutter suppression and instability response enhancement. The results demonstrate that the NES is most efficient and is most sensitive to changes in the stiffness when placed at the wingtip. For a given chordwise location, it is found that there is a range of flow speeds over which the NES is most effective and reducing the chordwise offset lowers the speed of the peak efficiency range and moves it closer to the flutter speed. In addition, increasing the stiffness coefficient of the NES improves the efficiency of the device in the immediate post-flutter region. Two near optimum NES devices are proposed with a mass ratios of 1% (located at the wingtip) and 2.5% (located at 75% span). Both of these improve the flutter speed by 5%, and reduce the post-flutter response by 64.5% and 59.2%, respectively.

中文翻译：

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具有非线性能量汇的飞机机翼的气动弹性


在本文中，研究了非线性能量汇对增强飞机机翼气动弹性稳定性和后不稳定响应的有效性。机翼在弯曲和扭转方面有两个自由度，并使用具有硬化非线性的扩展 Euler-Bernoulli 梁理论进行建模。非线性能量汇 （NES） 吸收器嵌入机翼内部，沿翼展分布。机翼附加的非稳态空气动力学载荷使用 Wagner 的指示升力模型进行模拟。机翼的结构动力学是使用扩展汉密尔顿原理推导的，并使用 Galerkin 方法进行离散化。NES 质量通过线性阻尼器和具有立方刚度非线性的非线性弹簧连接到翼梁。然后将耦合的气动弹性方程转换为状态空间。然后，进行数值积分以解决机翼的弯曲和扭转响应，以研究嵌入式 NES 的翼展和弦向位置对颤振抑制和不稳定响应增强的影响。结果表明，当放置在翼尖时，NES 是最有效的，并且对刚度的变化最敏感。对于给定的弦向位置，发现 NES 在一定流速范围内最有效，并且减小弦偏移会降低峰值效率范围的速度，使其更接近颤振速度。此外，增加 NES 的刚度系数可以提高器件在颤振后区域的效率。提出了两种接近最佳的 NES 器件，质量比为 1%（位于翼尖）和 2.5%（位于 75% 跨度）。这两者都将颤振速度提高了 5%，并将后颤振响应降低了 64.5% 和 59。2%。