High-frequency vibrations of circular and annular plates with the Mindlin plate theory

  • Hui Chen
  • Rongxing Wu
  • Longtao Xie
  • Jianke Du
  • Lijun Yi
  • Bin Huang
  • Aibing Zhang
  • Ji WangEmail author


Circular and annular elastic plates have wide applications as essential elements in various engineering structures and products demanding accurate analysis of their vibrations. At higher frequencies, the analysis of vibrations needs appropriate equations, as shown by the Mindlin plate equations for rectangular plates with tailored applications for the analysis of quartz crystal resonators. Naturally, there are equally strong demands for the equations and applications in circular and annular plates with the consideration of higher-order vibration modes. By following the procedure established by Mindlin based on displacement expansion in the thickness coordinate, a set of higher-order equations of vibrations of circular and annular plates are derived and truncated for comparisons with classical and first-order plate equations of circular plates. By utilizing these equations, coupled thickness-shear and flexural vibrations of circular and annular plates are analyzed for vibration frequencies and mode shapes.


Plate Mindlin Vibration Circular Frequency 



This research is supported in part by the National Natural Science Foundation of China (Grant Nos. 11372145 and 11672142). Additional funding is from the National Key R&D Program of China (Grant No. 2017YFB1102900). It was also supported by the Research Project Foundation of Zhejiang Educational Department (Grant No. Y201636501). The authors also received financial support from the K. C. Wong Magna Fund established and administered by Ningbo University.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Piezoelectric Device Laboratory, School of Mechanical Engineering and MechanicsNingbo UniversityNingboChina
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of MissouriColumbiaUSA
  3. 3.Department of Architectural EngineeringNingbo PolytechnicBeilun District, NingboChina

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