Wu Qikai, Cui Chunyang, Bertrand Thibault, Shattuck Mark D, O'Hern Corey S
Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA.
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, 100084 Beijing, China.
Phys Rev E. 2019 Jun;99(6-1):062901. doi: 10.1103/PhysRevE.99.062901.
We employ numerical simulations to study active transistor-like switches made from two-dimensional (2D) granular crystals containing two types of grains with the same size but different masses. We tune the mass contrast and arrangement of the grains to maximize the width of the frequency band gap in the device. The input signal is applied to a single grain on one side of the device, and the output signal is measured from another grain on the other side of the device. Changing the size of one or many grains tunes the pressure, which controls the vibrational response of the device. Switching between the on and off states is achieved using two mechanisms: (1) pressure-induced switching where the interparticle contact network is the same in the on and off states and (2) switching through contact breaking. In general, the performance of the acoustic switch, as captured by the gain ratio and switching time between the on and off states, is better for pressure-induced switching. We show that in these acoustic switches the gain ratio between the on and off states can be larger than 10^{4} and the switching time (multiplied by the driving frequency) is comparable to that obtained recently for sonic crystals and less than that for photonic transistor-like switches. Since the self-assembly of grains with different masses into 2D granular crystals is challenging, we describe simulations of circular grains with small circular knobs placed symmetrically around the perimeter mixed with circular grains without knobs. Using umbrella sampling techniques, we show that grains with six knobs most efficiently form the hexagonal crystals that yield the largest frequency band gap. Using the simulation results, we estimate the time required for vibration experiments to generate granular crystals of millimeter-sized steel beads with maximal band gaps.
我们采用数值模拟方法来研究由二维（2D）颗粒晶体制成的类似晶体管的有源开关，该晶体包含两种尺寸相同但质量不同的颗粒。我们调整颗粒的质量对比度和排列方式，以最大化器件中频率带隙的宽度。将输入信号施加到器件一侧的单个颗粒上，并从器件另一侧的另一个颗粒测量输出信号。改变一个或多个颗粒的尺寸可调节压力，从而控制器件的振动响应。使用两种机制实现开态和关态之间的切换：（1）压力诱导切换，其中开态和关态下的粒子间接触网络相同；（2）通过接触断开进行切换。一般来说，对于压力诱导切换，由开态和关态之间的增益比和切换时间所表征的声学开关性能更好。我们表明，在这些声学开关中，开态和关态之间的增益比可以大于10^4，并且切换时间（乘以驱动频率）与最近在声子晶体中获得的结果相当，且小于类似光子晶体管的开关。由于将不同质量的颗粒自组装成二维颗粒晶体具有挑战性，我们描述了对带有围绕周边对称放置的小圆形旋钮的圆形颗粒与不带旋钮的圆形颗粒混合的模拟。使用伞形采样技术，我们表明具有六个旋钮的颗粒最有效地形成了产生最大频率带隙的六边形晶体。利用模拟结果，我们估计了振动实验生成具有最大带隙的毫米尺寸钢珠颗粒晶体所需的时间。
