比翱工程实验室丨用于宽频带缓解流致振动的共振超材料设计
来源：interNoise 2021
在过去的几十年中，为了降低进入车辆和飞机舱室的噪音水平，以获得更好的噪音舒适性，人们特别关注降低由气流诱导振动引起的噪音[1–3]。由流致振动引起的噪声问题通常在低频范围内占主导地位，其中存在最高能量含量[4,5]。不同的噪音、振动和声振粗糙度（NVH）解决方案已经被研究来解决这个噪声问题[6-8]。然而，除了在较低频率范围内表现不佳之外，这些措施通常会导致笨重的NVH解决方案[9]。因此，需要寻求低质量和低体积措施，以在低频率下实现理想的NVH降低性能，同时确保轻量化设计。
事实上，局部共振超材料（LRMs：Locally Resonant Metamaterials）已被证明是一种很有前景的解决方案，可在明确定义的频率范围内减少声振系统[10, 11]的流动引起的NVH行为，称为阻带，这是不允许自由波传播的频率区[12]。可以通过在亚波长尺度上的主体结构上添加共振元件来实现[13]。
尽管如此，这些阻带通常在有限的频率范围内具有积极影响，并且考虑到此类激励类型的宽带特性，需要使用其他技术来使LRM解决方案在阻带频率范围之外更有利地执行。为此，这项工作提出了一种在空气动力学激励下对LRM结构的宽带振动声学行为进行数值建模和优化的方法。为了实现这一目标，使用由两个规则间隔的谐振附加网格组成的板的有限元(FE)模型：(i)第一个网格包含调谐到相同标称频率的谐振元件，以实现阻带行为和(ii)对于第二个网格，通过优化找到每个谐振器的调谐频率，以减少阻带区域外主体结构的振动响应。为了加速优化过程，使用了模型降阶(MOR)方案，即Craig-Bampton方法[14]。
为了说明研究中的空气动力学激励，在实验流设置中测量了由于掠流引起的频率相关压力波动，并将其用作数值模型中的力激励。鉴于未来的实验验证，选择这种方法来重现更真实的激发条件。
研究创新
该项研究提出了一种有限谐振超材料板（Finite Resonant Metamaterial Plate）的设计方法和一种对局部共振超材料（LRM）板进行数值建模和优化的方法，以实现对流致振动的宽带缓解。
图文快览
表1：钢板的材料特性
图1：a) 麦克风阵列和b) 施加载荷的板的有限元网格的表示
图2：在U=19 m/s的掠流激发下裸板的RMS PSD速度
图3：谐振器图案和可实现的单元的示意图
表2：聚甲基丙烯酸甲酯（PMMA）的材料特性
图4：a)谐振器设计b)谐振器的平面外弯曲模态，用于创建阻带和c)具有不同尺寸的谐振器的图示
图5：单谐振器型（SRT）情况下的频散图，其中灰色阴影区域表示预测的阻带。还描绘了不可约布里渊轮廓的表示以及相应波空间的草图
图6：板和谐振器的草图，用于模型降阶（MOR）的可视化表示。属于板的深绿色区域和谐振器灰色区域的节点的自由度被压缩。保留节点的自由度：连接区域（板上的浅绿色区域），施力位置（红点），单元格交叉点和谐振器的基极连接区
图7：建立和优化共振超材料结构数值模型的主要步骤草图，以实现降低宽频带流致振动
图8：在U=19 m/s的掠流激励下，具有用于网格B的谐振器优化配置的裸板、SRT和板的RMS PSD速度比较。右侧说明了网格B的频率分布
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