Yang Shuai, Liu Ying, Gu Yu, Yang Qingshan
Department of Mechanics, School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China.
Soft Matter. 2014 Jun 21;10(23):4110-7. doi: 10.1039/c3sm53206b.
In this paper, Rayleigh wave propagation in nematic elastomers (NEs) is investigated. Characteristic equations for Rayleigh waves in the NEs are derived based on the viscoelastic theory of nematic elastomers in the low-frequency (hydrodynamic) limit. The dispersion and attenuation properties of the Rayleigh waves in the NEs are analyzed numerically. By considering the effects of the director, the rubber relaxation time and the dynamic soft elasticity of the NEs on the propagation characteristics of the Rayleigh waves are investigated. Results show that unlike Rayleigh waves in pure viscous materials, the Rayleigh wave displays obvious frequency dependence due to the dynamic soft elasticity of the NEs. There exists a critical transition frequency above which the Rayleigh wave velocity is gradually increased to a stable value, and at this frequency the Rayleigh wave velocity is temperature independent. The transition critical frequency where liquid behavior changes to rubber performance is director rotation time dependent, whilst the rubber relaxation time has less of an effect on its value. Although the particle trace is still elliptically polarized, the direction of the major axis is frequency and depth dependent. Clarification of these particular properties of Rayleigh waves is helpful for the further acoustic application of Rayleigh waves in NEs.
本文研究了向列型弹性体（NEs）中瑞利波的传播。基于向列型弹性体在低频（流体动力学）极限下的粘弹性理论，推导了NEs中瑞利波的特征方程。对NEs中瑞利波的频散和衰减特性进行了数值分析。通过考虑指向矢、橡胶松弛时间和NEs的动态软弹性对瑞利波传播特性的影响进行了研究。结果表明，与纯粘性材料中的瑞利波不同，由于NEs的动态软弹性，瑞利波表现出明显的频率依赖性。存在一个临界转变频率，高于该频率时瑞利波速度逐渐增加到一个稳定值，且在此频率下瑞利波速度与温度无关。液体行为转变为橡胶性能的转变临界频率取决于指向矢旋转时间，而橡胶松弛时间对其值的影响较小。虽然质点轨迹仍为椭圆偏振，但长轴方向与频率和深度有关。阐明瑞利波的这些特殊性质有助于瑞利波在NEs中的进一步声学应用。
