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首页> 外文期刊>International journal of non-linear mechanics >Effect of non-linear damping on the structural dynamics of flapping beams
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Effect of non-linear damping on the structural dynamics of flapping beams

机译：非线性阻尼对拍梁结构动力学的影响

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In this paper we investigate, through experiment and simulation, the effects of non-linear damping forces on the large amplitude structural dynamics of slender cantilever beams undergoing flapping motion in air. The aluminum beams are set into flapping motion through actuation at the beam base via a 4-bar crank-and-rocker mechanism. The beam strain response dynamics are investigated for two flapping amplitudes, 15° and 30°, and a range of flapping frequencies up to 1.3 times the first modal frequency. In addition to flapping at standard air pressure, flapping simulations and experiments are also performed at reduced air pressure (70% vacuum). In the simulations, linear and non-linear, internal and external damping force models in different functional forms are incorporated into a non-linear, inextensible beam theory. The external non-linear damping models are assumed to depend, parame-trically, on ambient air density, beam width, and an empirically determined constant. Periodic solutions to the model equation are obtained numerically with a 1-mode Galerkin method and a high order time-spectral scheme. The effect of different damping forces on the stability of the computed periodic solutions is analyzed with the aid of Floquet theory. The strain-frequency response curves obtained with the various damping models suggest that, when compared to the linear viscous and non-linear internal damping models, the non-linear external damping models better represent the experimental damping forces in regions of primary and secondary resonances. In addition to providing improved correlation with experimental strain response amplitudes over the tested range of flapping frequencies, the nonlinear (external) damping models yield stable periodic solutions for each flapping frequency which is consistent with the experimental observations. Changes in both the experimental ambient pressure and flapping amplitude are determined to result in some variation in the non-dimensional parameters associated with each of the non-linear external damping models. This result likely indicates an incomplete description of the model parameter dependence and/or non-linear functional form of the damping force.
机译：在本文中，我们通过实验和仿真研究了非线性阻尼力对细长悬臂梁在空气中拍打运动的大振幅结构动力学的影响。铝梁通过4杆曲柄和摇杆机构在梁基座处致动，从而使其拍打运动。研究了两个拍幅幅度15°和30°以及最高到第一模态频率1.3倍的拍幅频率范围的光束应变响应动力学。除了在标准气压下拍打外，还在降低的气压（70％真空）下执行拍打模拟和实验。在仿真中，将线性和非线性，内部和外部不同功能形式的阻尼力模型合并到非线性，不可扩展的梁理论中。假定外部非线性阻尼模型在参数上取决于环境空气密度，束宽度和凭经验确定的常数。使用一模Galerkin方法和高阶时间谱方案以数值形式获得模型方程的周期解。借助Floquet理论，分析了不同阻尼力对计算周期解稳定性的影响。通过各种阻尼模型获得的应变频率响应曲线表明，与线性粘性和非线性内部阻尼模型相比，非线性外部阻尼模型更好地表示了一次和二次共振区域的实验阻尼力。除了在拍击频率的测试范围内改善与实验应变响应幅度的相关性之外，非线性（外部）阻尼模型还为每个拍击频率提供了稳定的周期解，这与实验观察结果一致。确定实验环境压力和拍打幅度的变化，以导致与每个非线性外部阻尼模型关联的非维数参数发生某些变化。该结果可能表明对模型参数的依赖性和/或阻尼力的非线性功能形式的描述不完整。

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