On the correction of the higher-order Mindlin plate theory

Ji, Wang; Yu, Jiun-Der; Yong, Yook‐Kong

doi:10.3233/jae-2005-693

Cited by 31 publications

(21 citation statements)

References 13 publications

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“…The correction factors for Mindlin's third and fifth order plate theories were determined in ref. [14] so that exact cutoff frequencies of the relevant waves can be predicted. Effects of the inertia and stiffness of metal electrodes on frequencies of crystal plates were considered in the 2D theory of plates in ref.…”

Section: Structural Theoriesmentioning

confidence: 98%

Analytical and numerical modeling of resonant piezoelectric devices in China-A review

Yang

2008

Sci. China Ser. G-Phys. Mech. Astron.

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The results on theoretical and numerical modeling of resonant piezoelectric devices in China are reviewed. Solutions to dynamic problems of the propagation of bulk acoustic waves (BAW), surface acoustic waves (SAW), vibrations of finite bodies, and analyses of specific devices are discussed. Results from both the ultrasonics community and mechanics researchers are included. It is hoped that the paper will be useful for the understanding, communication and collaboration between Chinese and foreign scholars. The paper may also be helpful for bridging the gap between ultrasonics and mechanics researchers on piezoelectricity research. The paper contains 316 references.

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Section: Structural Theoriesmentioning

confidence: 98%

Analytical and numerical modeling of resonant piezoelectric devices in China-A review

Yang

2008

Sci. China Ser. G-Phys. Mech. Astron.

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“…Of course, the Lee plate theory based on the trigonometric expansion is similar in nature and also offers equally accurate results of analysis as an alternative approach [24][25][26][27][28][29][30][31][32]. Consequently, many efforts have been made on the correction, truncation, and simplification of the Mindlin plate theory with extensive work on AT-cut quartz crystal plates with and without electrodes for resonator applications by Wang and collaborators [15][16][17][18][19]. The finite element method (FEM) is also implemented with the Mindlin plate equations for the numerical analysis of crystal plates, making it possible for us to examine the plate equations in detail and also deal with the twodimensional problems more efficiently [33,34].…”

Section: Introductionmentioning

confidence: 97%

“…From our studies on the higher-order Mindlin plate equations for vibrations of overtone modes of AT-cut quartz crystal plates [9][10][11], a complete procedure on the correction and truncation of the Mindlin plate equations has been established and correction factors up to the fifth-order have been obtained for both analytical and FEM procedures [15][16][17]. In the analytical process, we have also found that the higher-order equations with correction procedure and factors are applicable to the analysis of thickness-shear vibrations of SC-cut quartz crystal plate [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…From the beginning, it has been widely utilized in the vibration analysis of different kinds of piezoelectric plates with the AT-cut of quartz crystal as a typical example [8][9][10][11][12][13][14]. For couplings of flexural and thickness-shear modes in finite crystal plates, a correction of Mindlin plate theory through inserting correction factors for Y-and AT-cut quartz crystal plates were done by Mindlin and others [15][16][17][18][19], effectively extending the corrected plate theory to include the thickness-twist, face-extension, and face-shear modes. The improved Mindlin plate theory is used for the analysis of crystal plates in the fundamental and overtone TSh vibrations including the consideration of effects of electrodes, temperature variation, and even the viscosity [9][10][11][12][13][14][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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Free and forced vibrations of SC-cut quartz crystal rectangular plates with the first-order Mindlin plate equations

Wang

Chen

et al. 2017

Ultrasonics

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“…For the analysis with the Mindlin plate theory, Wang [5,10,11] have the plate equations corrected without and with mass effect of electrodes considered. The inclusion of stiffness effect was demonstrated before and the calculation is carried out in this study as part of the continued refinement of plate equations for the analysis of quartz crystal resonator.…”

Section: Introductionmentioning

confidence: 99%

Correction factors for the Mindlin plate equations for thickness vibrations of crystal plates with thicker electrodes

Huang

Chen

et al. 2013

2013 Joint European Frequency and Time Forum &Amp; International Frequency Control Symposium (EFTF/IFC)

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The Mindlin plate theory has been widely used for the study of high frequency vibrations of quartz crystal plates for resonator design and analysis. To improve the accuracy, the plate equations have to be corrected for the exact thickness-shear frequencies which in turn ensure the accurate results for other coupled modes. The correction procedure was suggested by Mindlin and the correction factors for the firstorder equations have been available. Lately, a systematic procedure for the correction factors up to the fifth-order has been established and two correction schemes with different correction factors have been adopted for the higher-order vibrations. These results have expanded applications of the Mindlin plate equations to the overtone vibration analysis which is required for the overtone resonators. One critical issue concerning the applications of the Mindlin plate with correction factors are the effect of electrodes, which are essential part of resonators and complications are resulted. With this objective in mind, we start from the Mindlin plate equations with a full set of vibration modes for the consideration of electrode mass and stiffness effects as a continuation of our earlier studies which only considered the mass effect in terms of mass ratios. The analysis regarding to the AT-cut of quartz crystal plates show that the consideration of electrode stiffness and mass will change the correction factors, thus making the equations more accurate in the calculation of frequency spectra and mode shapes. For very thin electrodes, the correction factors should be the same as suggested by earlier studies. The procedure is implemented to the SC-cut quartz crystal plates which have more enhanced couplings of vibration modes due to the material anisotropy. Correction factors for both AT-and SC-cut quartz crystal plates with consideration of electrode stiffness are given in polynomials of mass ratios for different metals.

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On the correction of the higher-order Mindlin plate theory

Cited by 31 publications

References 13 publications

Analytical and numerical modeling of resonant piezoelectric devices in China-A review

Analytical and numerical modeling of resonant piezoelectric devices in China-A review

Free and forced vibrations of SC-cut quartz crystal rectangular plates with the first-order Mindlin plate equations

Correction factors for the Mindlin plate equations for thickness vibrations of crystal plates with thicker electrodes

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