In-plane free vibration of circular annular disks

S. Bashmal*, R. Bhat, S. Rakheja

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


This paper presents a generalized formulation for the in-plane modal characteristics of circular annular disks under combinations of all possible classical boundary conditions. The in-plane free vibration of an elastic and isotropic disk is studied on the basis of the two-dimensional linear plane stress theory of elasticity. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the natural frequencies and associated mode shapes. Two approaches have been used to represent a clamped boundary condition. The first approach assumes a polynomial expression that satisfies the clamped conditions, while the second approach uses a disk with free boundary supported on artificial springs with stiffness tending to infinity. The natural frequencies are tabulated and compared with data available in the literature. Mode shapes are presented to illustrate the free vibration behavior of the disk.

Original languageEnglish
Pages (from-to)216-226
Number of pages11
JournalJournal of Sound and Vibration
Issue number1-2
StatePublished - 24 Apr 2009
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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