NDLI: The fifth-order overtone vibrations of quartz crystal plates with higher-order Mindlin plate equations

Content Provider	IEEE Xplore Digital Library
Author	Ji Wang Lijun Yang Nisha Sun Rongxing Wu Jianke Du Dejin Huang
Copyright Year	2009
Description	Author affiliation: Piezoelectric Device Laboratory, School of Engineering, Ningbo University, 818 Fenghua Road, Zhejiang 315211, CHINA (Ji Wang; Lijun Yang; Nisha Sun; Rongxing Wu; Jianke Du; Dejin Huang)
Abstract	As demands for high frequency quartz crystal resonators rise, we are prompted to design and make overtone devices with the same material, process, and technology. Indeed, high-order overtone resonators have been widely utilized in many applications and further demands in precision products are also growing. The design of overtone resonators and further improvement of the existing ones to meet precision requirements are largely based on empirical approaches, but we found that the technique can be polished with theoretical and analytical efforts as we examine the applications of the Mindlin plate theory in the design and analysis of the fundamental type. Through the extensive improvements of the Mindlin plate theory, we can now analyze the vibration mode couplings, electrode effect, optimal sizes, and thermal behavior, among others. These essential analytical procedures have been implemented in finite element analysis tools with more advanced features such as the nonlinear behavior prediction and eventually circuit parameter extraction. Since it has been proven that the Mindlin plate equations can be used for the vibration analysis of plates at the higher-order overtone modes with accurate prediction of frequency and dispersion relations in the vicinity of cut-off frequencies, we extended the equations to the third-order for the modal behavior and frequency spectra. The results show that earlier knowledge on the proper selection of the sizes of electrode can be proven from our analysis. In addition, the spatial variation and end effects of displacements, particularly of the working mode, can be used in the optimal selection of resonator configuration. The design changes can be used as a way to improve the resonator performance, which has been increasingly degenerating for higher-order overtone types, to meet more stringent requirements. We now extend the plate equations to the fifth-order so the design principle and guidelines can be summarized from more analytical results of overtone vibrations. These predictions on frequency, deformation, and electrode effects from studies with successive orders of equations can be used for resonator design at higher overtone frequencies.
Starting Page	455
Ending Page	459
File Size	533196
Page Count	5
File Format	PDF
ISBN	9781424435111
ISSN	10756787
DOI	10.1109/FREQ.2009.5168221
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-04-20
Publisher Place	France
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Harmonic analysis Electrodes Cutoff frequency Nonlinear equations Resonant frequency Crystalline materials Coupling circuits Finite element methods Parameter extraction Dispersion
Content Type	Text
Resource Type	Article

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