Centrifugal forces enable band gaps that self-adapt to synchronous vibrations in rotating elastic metamaterial
Centrifugal forces enable band gaps that self-adapt to synchronous vibrations in rotating elastic metamaterial
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DOI：
10.1016/j.ymssp.2023.110689
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发表时间：
2023-08-20
影响因子：
8.4
通讯作者：
Matlack，Kathryn H.
中科院分区：
文献类型：
--
作者：
Arretche，Ignacio;Matlack，Kathryn H.
机械系统的旋转可以极大地改变其模态和波传播响应。在经典的傅科摆的例子中，来自地球自转的科里奥利力导致摆的路径在地球上的观察者看来是偏转的。最近，来自旋转的科里奥利力和陀螺效应已被证明打破时间反演对称性，诱导非互易性，并改变声子晶体的能带结构。然而，旋转也会引入离心力，离心力会通过应力硬化和自旋软化效应显著影响振动响应。虽然这在转子动力学领域得到了很好的研究，但离心力对声学超材料（AM）动力学行为的影响仍未得到探索。本文研究了具有局部共振的旋转轴中扭转带隙对转速的依赖关系。与以往的研究不同，我们明确地考虑了应力刚化的影响，在局部共振的旋转AM的降阶模型中引入应力刚化函数。然后，我们计算梁尖质量谐振器的应力硬化函数，并表明，这些谐振器有一个谐振频率，在渐近极限的旋转速度线性缩放，这反过来又导致AM的带隙线性依赖于旋转速度。激励旋转机械中的同步振动的存在，其中频率也是线性依赖于转速，我们表明，这种旋转AM支持带隙，自调整的同步振动频率，从而在很宽的频率范围内的衰减，从而旋转速度。最后，我们使用三维有限元分析验证了旋转AM的降阶模型。这项工作有助于对AM中旋转效应的基本理解，并在AM和转子动力学社区之间建立联系，有可能在转子动力学问题中引入新的振动控制。
The rotation of mechanical systems can greatly change their modal and wave propagation response. In the classic example of the Foucault pendulum, the Coriolis force from the Earth’s rotation causes the pendulum path to appear deflected to an observer on Earth. More recently, Coriolis forces and gyroscopic effects from rotation have been shown to break time-reversal symmetry, induce non-reciprocity, and change the band structure of phononic crystals. However, rotation also introduces centrifugal forces that can considerably affect the vibration response through stress stiffening and spin softening effects. Although this is well studied in the field of rotor dynamics, the effects of centrifugal forces on the dynamic behavior of acoustic metamaterials (AMs) are still unexplored. In this paper, we study the dependence of torsional band gaps on rotational speed in a rotating shaft with attached local resonances. Different from previous studies, we explicitly consider the effects of stress stiffening in local resonances by introducing a stress stiffening function in a reduced order model of the rotating AM. We then calculate the stress stiffening function for beam-tip-mass resonators and show that these resonators have a resonant frequency that scales linearly with the rotational speed in the asymptotic limit, which in turn causes the band gaps of the AM to depend linearly on the rotational speed. Motivated by the presence of synchronous vibrations in rotating machinery, in which frequency is also linearly dependent on rotational speed, we show that this rotating AM supports band gaps that self-adjust to the synchronous vibration frequency, resulting in attenuation over a wide range of frequencies and thus rotational speeds. Finally, we validate the reduced order model of the rotating AM using 3D finite element analysis. This work contributes a foundational understanding of the effects of rotation in AMs and builds a connection between the AM and rotor dynamics communities, with the potential to introduce novel vibration control in rotor dynamics problems.