Huang Yunke, Hou Hong, Oterkus Selda, Wei Zhengyu, Gao Nansha
Key Laboratory of Ocean Acoustics and Sensing, School of Marine Science and Technology, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi'an, Shaanxi 710072, China.
Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, 100 Montrose Street, Glasgow, G4 0LZ, United Kingdom.
J Acoust Soc Am. 2020 Jan;147(1):428. doi: 10.1121/10.0000580.
This study focuses on the two-dimensional (2-D) finite-difference time-domain (FDTD) formulations to investigate the acoustic wave propagation in elastomers contained in a fluid region under different thermal conditions. The developed FDTD formulation is based on a direct solution of the time-domain wave equation and the Havriliak-Negami (H-N) dynamic mechanical response of the elastomers. The H-N representation, including double fractional derivative operators, can be accurately transferred from the frequency-domain to the time-domain by using Riemann-Liouville theory and the Grunwald-Letnikov operator for fractional derivative approximations. Since the Williams-Landel-Ferry shift function is related to the relaxation time for different thermal conditions, the proposed scheme represents a simple and accurate prediction of acoustic wave propagation for varying thermal conditions. The pulse-wave propagation in a viscous fluid field is simulated by investigating the Navier-Stokes equations. The acoustic properties of different elastomers in a variety of temperatures are obtained by means of the proposed FDTD formulation and validated by a good agreement with the experimental data over a wide frequency range. Additionally, the 2-D examples relevant to wave propagation in different elastomers contained in a fluid field are implemented. The proposed FDTD formulation can be used to predict 2-D acoustic wave propagation in different thermal conditions accurately.
本研究聚焦于二维时域有限差分（FDTD）公式，以研究在不同热条件下流体区域中弹性体内的声波传播。所开发的FDTD公式基于时域波动方程的直接求解以及弹性体的哈夫里利亚克 - 内加米（H-N）动态力学响应。通过使用黎曼 - 刘维尔理论和用于分数阶导数近似的格鲁恩瓦尔德 - 莱蒂尼科夫算子，包含双分数阶导数算子的H-N表示可以准确地从频域转换到时域。由于威廉姆斯 - 兰德尔 - 费里移位函数与不同热条件下的弛豫时间相关，所提出的方案为不同热条件下的声波传播提供了简单而准确的预测。通过研究纳维 - 斯托克斯方程来模拟粘性流体场中的脉搏波传播。借助所提出的FDTD公式获得了不同温度下不同弹性体的声学特性，并通过在宽频率范围内与实验数据的良好吻合进行了验证。此外，还实现了与流体场中不同弹性体内波传播相关的二维示例。所提出的FDTD公式可用于准确预测不同热条件下的二维声波传播。
