Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA.
Phys Rev E. 2017 Jun;95(6-1):063002. doi: 10.1103/PhysRevE.95.063002. Epub 2017 Jun 21.
The governing equation for elastic waves in flexural plates is not form invariant, and hence designing a cloak for such waves faces a major challenge. Here, we present the design of a perfect broadband cloak for flexural waves through the use of a nonlinear transformation in the region of the cloak and by matching term by term the original and transformed equations and also assuming a prestressed material with body forces. For a readily achievable flexural cloak in a physical setting, we further present an approximate adoption of our perfect cloak under more restrictive physical constraints. Through direct simulation of the governing equations, we show that this cloak, as well, maintains a consistently high cloaking efficiency over a broad range of frequencies. The methodology developed here may be used for steering waves and designing cloaks in other physical systems with non-form-invariant governing equations.
弯曲板中弹性波的控制方程不是形式不变的，因此设计这种波的斗篷面临着重大挑战。在这里，我们通过在斗篷区域使用非线性变换，并通过逐项匹配原始和变换方程，同时假设具有体力的预应力材料，为弯曲波设计了一个完美的宽带斗篷。对于物理环境中更容易实现的弯曲斗篷，我们进一步根据更严格的物理约束来近似采用我们的完美斗篷。通过对控制方程的直接模拟，我们表明这种斗篷在很宽的频率范围内也能保持始终如一的高隐身效率。这里开发的方法可用于控制波和在具有非形式不变控制方程的其他物理系统中设计斗篷。
