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. 2024 Jan 22;10:13. doi: 10.1038/s41378-023-00646-5

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© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 3 — a Diagram of measurement sites recorded by laser Doppler vibrometer. b (Left) Reconstruction of the actuator vibration obtained from laser vibrometer measurements at the points in a. (Right) The mode shapes generated from the ANSYS simulation, showing agreement between simulation and measurement. c PZT thin film thickness measured using a profilometer at sites A1–A4. d Comparison of vertical displacement (Uz) between simulation and experimental results