Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78758, USA.
Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712-1591, USA.
Phys Rev E. 2019 Jan;99(1-1):013001. doi: 10.1103/PhysRevE.99.013001.
Acoustic nonreciprocity has been shown to enable a plethora of effects analogous to phenomena seen in quantum physics and electromagnetics, such as immunity from backscattering and unidirectional band gaps, which could lead to the design of direction-dependent acoustic devices. One way to break reciprocity is by spatiotemporally modulating material properties, which breaks parity and time-reversal symmetries. In this paper, we present a model for a medium in which a slow nonlinear deformation modulates the effective material properties for small overlaid disturbances (often referred to as "small-on-large" propagation). The medium is modeled as a discrete spring-mass chain that undergoes large deformation via prescribed displacements of certain points in the unit cell. A multiple-scale perturbation analysis shows that, for sufficiently slow modulations, the small-scale waves can be described by a linear monatomic chain with time- and space-dependent on-site stiffness. The modulation depth can be tuned by changing the geometric and stiffness parameters of the unit cell. The accuracy of the small-on-large approximation is demonstrated using direct numerical simulations.
声学非互易性已经被证明可以实现类似于量子物理和电磁学中看到的多种效应，例如对背散射的免疫和单向带隙，这可能导致设计依赖于方向的声设备。打破互易性的一种方法是通过时空调制材料特性，从而打破奇偶和时间反转对称性。在本文中，我们提出了一种介质模型，其中慢非线性变形调制小叠加扰动（通常称为“大对小”传播）的有效材料特性。该介质被建模为一个离散的弹簧-质量链，通过单元中某些点的规定位移来经历大变形。多尺度微扰分析表明，对于足够慢的调制，小尺度波可以用具有时间和空间相关局域刚度的线性单原子链来描述。通过改变单元的几何和刚度参数可以调整调制深度。使用直接数值模拟验证了大对小逼近的准确性。
