Tunable and reconfigurable mechanical transmission-line metamaterials via direct active feedback control
Tunable and reconfigurable mechanical transmission-line metamaterials via direct active feedback control
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DOI：
10.1016/j.ymssp.2019.01.001
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发表时间：
2019-05
影响因子：
8.4
通讯作者：
L. Sirota;F. Semperlotti;A. Annaswamy
中科院分区：
文献类型：
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作者：
L. Sirota;F. Semperlotti;A. Annaswamy
我们考虑的问题，使用主动反馈控制，以创建可调和可重构的机械超材料能够支持非常规的波传播机制。标称系统选择用于此分析是一个一维均匀杆具有周期性分布的力致动器和受纵向波。我们注意到，该系统没有利用局部夹杂物，而是将致动器直接连接到梁上，并通过周期性施加的力来实现超材料特性。我们设计的控制算法，以实现所需的本构参数的超材料在闭环。特别地，控制系统被设计为生成零或负值的有效属性（即刚度和质量），以获得具有不同动态行为的超材料。在这项研究中，考虑了四种不同的制度的有效属性：单负或零，双负，双零，双正。因此，通过直接控制方法可实现的本构参数仅由反馈算法定义，并且不限于否则将由局部谐振器施加的任何特定性质。我们的模型和分析的分数阶传递函数，这显着表现出的特殊特性的超材料，包括本构参数，色散，传输和反射特性。我们通过数值仿真说明了控制系统的稳定性和性能。最后，我们注意到，尽管在这项研究中使用的机械系统的选择，所提出的结果具有普遍适用性，所有这些系统所描述的二阶波动方程在其名义上的非受控状态。
We consider the problem of using active feedback control to create tunable and reconfigurable mechanical metamaterials capable of supporting unconventional wave propagation mechanisms. The nominal system chosen for this analysis is a one-dimensional homogeneous bar having periodically distributed force actuators and subject to longitudinal waves. We note that this system does not make use of local inclusions, instead the actuators are attached directly to the beam and achieve metamaterial properties by means of periodically applied forces. We design control algorithms in order to achieve desired constitutive parameters for the metamaterial in closed loop. In particular, the control system is designed to generate either zero or negative values of the effective properties (i.e. stiffness and mass) to obtain a metamaterial with different dynamic behaviors. Four different regimes of effective properties are considered in this study: single negative or zero, double negative, double zero, double positive. The constitutive parameters achievable via the direct control approach are therefore defined only by the feedback algorithms and are not confined to any particular properties that would otherwise be imposed by local resonators. We model and analyze the system by fractional order transfer functions, which explicitly exhibit the special characteristics of the metamaterial, including the constitutive parameters, dispersion, and transmission and reflection properties. We illustrate the stability and performance of the control system through numerical simulations. Finally we note that, despite the choice of the mechanical system used in this study, the proposed results have general applicability to all those systems described by the second order wave equation in their nominal uncontrolled state.