Jaglinski Tim, Lakes Roderic S
Engineering Mechanics Program, Department of Engineering Physics, University of Wisconsin, Madison, Wisconsin 53706-1687, USA.
Rev Sci Instrum. 2011 Mar;82(3):035105. doi: 10.1063/1.3559305.
Mode structure maps for freely vibrating cylinders over a range of Poisson's ratio, ν, are desirable for the design and interpretation of experiments using resonant ultrasound spectroscopy (RUS). The full range of isotropic ν (-1 to +0.5) is analyzed here using a finite element method to accommodate materials with a negative Poisson's ratio. The fundamental torsional mode has the lowest frequency provided ν is between about -0.24 and +0.5. For any ν, the torsional mode can be identified utilizing the polarization sensitivity of the shear transducers. RUS experimental results for materials with Poisson's ratio +0.3, +0.16, and -0.3 and a previous numerical study for ν = 0.33 are compared with the present analysis. Interpretation of results is easiest if the length∕diameter ratio of the cylinder is close to 1. Slight material anisotropy leads to splitting of the higher modes but not of the fundamental torsion mode.
对于使用共振超声光谱法（RUS）进行实验的设计和结果解释而言，一系列泊松比ν下自由振动圆柱体的模态结构图是很有必要的。本文采用有限元方法分析了各向同性ν的全范围（-1至+0.5），以适应具有负泊松比的材料。只要ν在约-0.24至+0.5之间，基本扭转模态就具有最低频率。对于任何ν，都可以利用剪切换能器的偏振灵敏度来识别扭转模态。将泊松比为+0.3、+0.16和-0.3的材料的RUS实验结果以及之前针对ν = 0.33的数值研究与当前分析进行了比较。如果圆柱体的长度∕直径比接近1，则结果解释最为容易。轻微的材料各向异性会导致高阶模态分裂，但基本扭转模态不会分裂。
