The determination of complex elastic, piezoelectric, and dielectric coefficients of piezoelectric ceramics is important for precision engineering devices. Here, a novel method for determining the optimal material coefficients is presented. This method minimizes the average relative error in the values of conductance, susceptance, resistance, and reactance obtained from the 1-D model in the IEEE Standard (ANSI/IEEE Std 176-1987) and the experimental measurements of the first and second radial modes. Poisson's ratio is assumed to be a complex number in addition to the elastic, piezoelectric, and dielectric coefficients in the present method. The global minimum of the average relative error is found by searching the minimum among all local minima of the average relative error, which are obtained with the Levenberg-Marquardt modification of Newton's method from randomly chosen initial conditions. The optimal material coefficients of an APC 850 disk and an APC 855 disk are calculated with this method. The uncertainties in the optimal material coefficients are evaluated by calculating the minimum average relative error when the real or imaginary part of each coefficient is prescribed.

中文翻译：

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一种评估径向振动模式下压电陶瓷复合材料系数的新方法。

压电陶瓷复合弹性、压电和介电系数的测定对于精密工程设备具有重要意义。在这里，提出了一种确定最佳材料系数的新方法。这种方法最大限度地减少了从 IEEE 标准 (ANSI/IEEE Std 176-1987) 中的一维模型以及第一和第二径向模式的实验测量值中获得的电导、电纳、电阻和电抗值的平均相对误差. 除了本方法中的弹性、压电和介电系数之外，泊松比被假定为复数。通过在平均相对误差的所有局部最小值中搜索最小值，找到平均相对误差的全局最小值，它们是从随机选择的初始条件通过牛顿方法的 Levenberg-Marquardt 修正获得的。APC 850 圆盘和 APC 855 圆盘的最佳材料系数就是用这种方法计算出来的。当规定每个系数的实部或虚部时，通过计算最小平均相对误差来评估最佳材料系数的不确定性。