Accurate measurement of elastic constants in resonant ultrasound spectroscopy (RUS) depends on a perfect matching in the calculated and measured mode frequencies of free vibration of the solid specimen under study. Calculation of these frequencies requires estimated values of the elastic constants of the material. The present work proposes and demonstrates a method to derive initial guess values of the essential parameters for an isotropic and homogeneous material from the acquired RUS spectra itself. Specimen samples are prepared in the shape of rectangular parallelepiped having nearly same cross-sectional dimension but with different lengths. For particular compression (shear) mode corresponding to length l , the frequency f is inversely proportional to l . The slope m of f versus 1/ l plot equals half of the compression (shear) velocity and this in turn gives an estimate of $$ c_{11} $$ c 11 ( $$ c_{44} $$ c 44 ). With these parameters as the input guess parameters, RUS fitting method is executed to find out the best fit results. $$ c_{44} $$ c 44 obtained in this way is a good estimate close to its actual value. Further refinement of the parameter values is achieved by identifying volume oscillation mode frequencies for various sample lengths from the best fit frequency table of RUS output. The slope m of f versus 1/ l plot for these modes corresponds to the bulk modulus (K). $$ c_{11} $$ c 11 calculated from K and $$ c_{44} $$ c 44 is a better estimate and a second step fitting method with these parameters as the input values gives final output values with improved accuracy. Elastic constants of commercially available specimens of aluminum, copper, lead, steel and brass are measured in this method assuming macroscopic homogeneity. Results are compared and found to be in good agreement with available literature values.

中文翻译：

---

超声共振光谱中各向同性弹性常数的估计和确定

谐振超声谱 (RUS) 中弹性常数的准确测量取决于所研究的固体样品的自由振动的计算和测量模式频率的完美匹配。计算这些频率需要材料弹性常数的估计值。目前的工作提出并演示了一种从获得的 RUS 光谱本身推导出各向同性和均质材料的基本参数的初始猜测值的方法。样品制备成长方体形状，具有几乎相同的横截面尺寸但具有不同的长度。对于对应于长度 l 的特定压缩（剪切）模式，频率 f 与 l 成反比。f 与 1/ l 曲线图的斜率 m 等于压缩（剪切）速度的一半，这反过来给出了 $$ c_{11} $$ c 11 ( $$ c_{44} $$ c 44 ) 的估计值。以这些参数作为输入猜测参数，执行RUS拟合方法以找出最佳拟合结果。$$ c_{44} $$ c 44 用这种方法得到的估计值很接近它的实际值。通过从 RUS 输出的最佳拟合频率表中识别各种样本长度的体积振荡模式频率来实现参数值的进一步细化。这些模式的 f 与 1/ l 曲线的斜率 m 对应于体积模量 (K)。$$ c_{11} $$ c 11 从 K 和 $$ c_{44} $$ c 44 计算出来是更好的估计，并且是使用这些参数的第二步拟合方法，因为输入值给出了具有改进精度的最终输出值。假定宏观均匀性，在该方法中测量市售铝、铜、铅、钢和黄铜试样的弹性常数。结果进行了比较，发现与可用的文献值非常吻合。