An exact solution for in-plane vibrations of an arch having variable curvature and cross section

Chiung-Shiann Huang*, Y. P. Tseng, A. W. Leissa, K. Y. Nieh

*Corresponding author for this work

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

An exact solution for in-plane vibration of arches with variable curvature as well as cross section has been developed using the famous Frobenius method combined with the dynamic stiffness method. The effects of shear deformation and rotary inertia are taken into account. A convergent solution is always guaranteed without numerical difficulties. An important by-product of this series solution is that the first known dynamic stiffness matrix for an arch with variable curvature and variable cross section is also explicitly formulated. Some new numerical results are given for non-dimensional frequencies of parabolic arches with a certain type of variation of cross section along the arch that is often used in practical structures. Extensive and accurate (six significant figure) non-dimensional frequency tables and graphic charts are presented for a series of parabolic arches showing the effects of rise to span length, slenderness ratio, and variation of cross section.

Original languageEnglish
Pages (from-to)1159-1173
Number of pages15
JournalInternational Journal of Mechanical Sciences
Volume40
Issue number11
DOIs
StatePublished - 1 Nov 1998

Keywords

  • Arch
  • Exact solution
  • Free vibration
  • Variable cross section
  • Variable curvature

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