Accurate determination of three types of losses (dielectric, elastic and piezoelectric) in piezoelectric materials is critical, since they are closely related to the performance of high-power piezoelectric devices. The Standard k33 mode has a number of serious deficits that hinders researchers from determining accurate physical parameters and losses. In order to overcome such deficits, partial electrode has been devised and proposed. This study provides analytical derivation process and proposes parameter determination method by utilizing analytical solutions. Compared to finite element analysis, analytical solutions show 0.1 % difference in resonance frequencies and 2 % difference in mechanical quality factors, proving them as valid modeling. The analytical solutions are fitted to experimental data to determine physical parameters and losses. The k33 (electromechanical coupling factor) values were calculated with determined values from curve fitting in two different ways and show good agreement to each other.

中文翻译：

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用于损耗表征的 k33 模式部分电极配置的分析建模

准确确定压电材料中的三种损耗（介电、弹性和压电）至关重要，因为它们与大功率压电器件的性能密切相关。Standard k33 模式有许多严重的缺陷，阻碍了研究人员确定准确的物理参数和损失。为了克服这种缺陷，已经设计并提出了部分电极。本研究提供了解析推导过程，并提出了利用解析解的参数确定方法。与有限元分析相比，解析解显示共振频率差异为 0.1%，机械品质因数差异为 2%，证明它们是有效的建模。解析解适合实验数据以确定物理参数和损耗。