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压电圆片径向方式等效线路的普遍形式

COMPLETE EQUIVALENT CIRCUIT FOR RADIAL MODE OF PIEZOELECTRIC DISKS

  • 摘要: 压电圆片径向方式振子在压电测量中得到广泛应用,国际上的压电测量标准均把它列为主要内容。这种振动方式,Mason曾作过详细研究,得到了电导纳表达式以及只适用于基频共振频率附近的简化等效线路。本文从Mason的电导纳表达式出发,利用Mittag-Leffler定理,导出了适用于任何频率的等效线路的普遍形式;从而证明了此种形式等效线路与从波动方程求得的严格解析解完全等价。

     

    Abstract: Radial mode resonator of a piezoelectric disk is extensively applied to piezoelectric measurement; It has been a major subject of piezoelectric measurement in international standardization. Mason researched this mode at first, and he derived the electrical admittance formula and approximate equivalent circuit that is only suitable to the vicinity of the fundmental frequency. In this article, based on the admittance formula derived by Mason and using the Mittag-Leffler's theorem, the complete equivalent circuit have been derived that is suitable to any frequency. It is proved that the complete equivalent circuit corresponds to the strict analytic solution derived from wave equation.

     

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