Energy Integration Method for Calculating keffand its Application in Design Optimization of Disk Resonators via Convex Edge

Qi Zhou, Wenwu Cao

Research output: Contribution to journalArticlepeer-review


Piezoelectric resonators have been extensively used as filters, actuator, and sensors. The effective electromechanical coupling coefficient ( {k}-{\text {eff}}{)} is the most useful parameter to evaluate the electromechanical conversion efficiency of piezoelectric resonators. However, even for simple geometry piezoelectric resonators, such as disks, the coupling between different modes makes the resonant characteristics very complex. The coupling causes low electromechanical coupling efficiency of the intended mode. We propose a finite-element-based energy integration method to calculate {k}-{\text {eff}} of piezoelectric resonators. This method is more accurate than the conventional resonance-Antiresonance method and provides a powerful tool for the design optimization of pure mode resonators. A special case studied here is the fundamental thickness extensional (TE) mode of PZT-8 disks in the aspect ratio range of 2-20. Our results showed that multimode coupling near this mode can be greatly suppressed by modifying the edge surface of the disk to a convex shape. Such an optimized design could enhance {k}-{\text {eff}} of the fundamental TE mode by as much as 10%-45% depending on the aspect ratio.

Original languageEnglish (US)
Article number9149677
Pages (from-to)734-741
Number of pages8
JournalIEEE transactions on ultrasonics, ferroelectrics, and frequency control
Issue number3
StatePublished - Mar 2021

All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering

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