https://doi.org/10.1140/epjs/s11734-025-01714-9
Regular Article
A new analytic model for free vibration of three-layer rectangular microcantilevers
State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, 116024, Dalian, China
a
dianxu@dlut.edu.cn
b
ruili@dlut.edu.cn
Received:
10
April
2025
Accepted:
26
May
2025
Published online:
13
June
2025
The three-layer rectangular microcantilever (TRM), with its enhanced mechanical performance and complex functional design, is widely applied in resonant sensors, actuators, and other devices in micro electromechanical systems. Studying its free vibration characteristics is essential for the design and optimization of these devices. Undoubtedly, an analytic model for the free vibration of the TRM based on the plate theory framework provides higher accuracy and broader applicability compared to the models based on the beam/torsion theories framework. However, due to the mathematical challenges in solving the high-order partial differential equations of the plate theory, the analytic model for the free vibration of the TRM commonly adopts the established frequency formulas based on the beam/torsion theories. In this way, developing a new accurate analytic model is important. This paper analytically solves the free vibration problem of a TRM based on the modified Hoff’s sandwich plate theory using the symplectic superposition method. The results reveal that the aspect ratio and Poisson’s ratio have a significant impact on the natural frequencies, and those based on the beam/torsion theories fail to accurately and comprehensively capture the free vibration characteristics of TRMs due to the neglect of certain bending effects. Comparison with both the references and refined finite element analysis validated the current results. The established analytic model is expected to serve as an accurate benchmark for the calibrating and verification of TRM resonant sensors.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
