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A unified procedure for free transverse vibration of rectangular and annular sectorial plates

  • Siyuan Bao
  • Shuodao WangEmail author
Original

Abstract

A unified solution procedure applicable for analyzing the free transverse vibration of both rectangular and annular sectorial plates is presented in this study. For the annular sectorial plate, the basic theory is simplified by a variable transformation in the radial direction. The analogies of coordinate system, geometry and potential energy between the two different shapes are drawn and then unified in one framework by introducing the shape parameter. A generalized solving procedure for the two shapes becomes feasible under the unified framework. The solution adopts the spectro-geometric form that has the advantage of describing the geometry of structure by mathematical or design parameters. The assumed displacement field and its derivatives are continuous and smooth in the entire domain, thereby accelerating the convergence. In this study, the admissible functions are formulated in simple trigonometric forms of the mass and stiffness matrices for both rectangular and annular sectorial plates can be obtained, thereby making the method computationally effective, especially for analyzing annular sectorial plates. The generality, accuracy and efficiency of the unified approach for both shapes are fully demonstrated and verified through benchmark examples involving classical and elastic boundary conditions.

Keywords

Rectangular plate Annular sectorial plate Transverse vibration Spectro-geometric method 

Notes

Acknowledgements

The authors acknowledge the support from the National Natural Science Foundation of China (Grant No. 11202146) and the Qinglan Project of JiangSu Province.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Civil EngineeringSuzhou University of Science and TechnologySuzhouChina
  2. 2.School of Mechanical and Aerospace EngineeringOklahoma State UniversityStillwaterUSA

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