Archive of Applied Mechanics

, Volume 89, Issue 11, pp 2215–2228 | Cite as

In-plane vibration of a circular ring with arbitrary concentrated elements by an analytical method

  • Mingchang NiuEmail author
  • Jinpeng Su
  • Zhenguo Zhang
  • Hongxing Hua


This paper investigates the vibration characteristics of a circular ring with an arbitrary number of concentrated elements based on the Hamilton principle. The shear and inertia effects are introduced to the variational functional of system kinetic and potential energy by adopting the generalized shell theory. The concentrated elements are treated as the concentrated masses with elastic boundary condition. The system vibration displacements are analytically expanded in the form of Fourier series and substituted into the variational functional to obtain the equation of motion. Computed results are compared with those solutions obtained from the finite element program ANSYS to validate the accuracy of the present method. Effects of the asymmetrical concentrated elements on the convergence of circumferential wavenumbers are discussed. Moreover, the coupling characteristics of different circumferential wavenumbers caused by the asymmetrical or symmetrical concentrated elements and their influences on the vibration response characteristics of the system under simple harmonic excitations are studied.


Vibration characteristics Circular ring Concentrated elements Circumferential wavenumber 



The authors are grateful to acknowledge that this study is financially supported by Institute of Vibration Shock and Noise, Shanghai Jiao Tong University.


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Copyright information

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

Authors and Affiliations

  • Mingchang Niu
    • 1
    Email author
  • Jinpeng Su
    • 1
  • Zhenguo Zhang
    • 1
  • Hongxing Hua
    • 1
  1. 1.State Key Laboratory of Mechanical System and Vibration, Institute of Vibration Shock and NoiseShanghai Jiao Tong UniversityShanghaiChina

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