The one‐dimensional radial vibration model of piezoelectric disks has been widely used to determine the relevant material coefficients from admittance measurements. However, the one‐dimensional model assumes infinitely thin disks, and therefore cannot predict their axial displacements. We extend the one‐dimensional model by performing an asymptotic analysis of the axisymmetric radial vibration of thin disks. The asymptotic expansions include the asymptotic axial displacement and the second‐order corrections to the admittance and the radial displacement in the one‐dimensional model. We verify the asymptotic expansions and the one‐dimensional model with the Chebyshev tau method. In the one‐dimensional model, the frequencies of the maximum admittance in the first and second radial modes are accurate to 1% for Pz27 disks with thickness‐to‐diameter ratios of 0.15 and 0.065, respectively. For a general piezoelectric disk in the forced vibration, the error of in the one‐dimensional model can be estimated from the second‐order correction of the asymptotic resonance frequency in the free vibration.

中文翻译：

---

薄压电盘径向振动的渐近分析

压电盘的一维径向振动模型已被广泛用于从导纳测量中确定相关的材料系数。但是，一维模型假设磁盘无限薄，因此无法预测其轴向位移。我们通过对薄盘的轴对称径向振动进行渐近分析来扩展一维模型。渐近展开包括一维模型中的渐进轴向位移和导纳和径向位移的二阶校正。我们使用Chebyshev tau方法验证渐近展开和一维模型。在一维模型中，最大导纳的频率对于厚度与直径之比分别为0.15和0.065的Pz27磁盘，第一和第二径向模式下的精度分别为1％。对于受迫振动的普通压电盘，可以通过自由振动中渐近共振频率的二阶校正来估算一维模型中的误差。