Axisymmetric vibrations of closed spherical shells: equations of motion and bifurcation analysis

We investigate the torsionless axisymmetric dynamics of a forced closed spherical shell. The non‐linear equations of motion are formulated using a variational approach and surface analysis. First, we revisit the linear eigenvalue problem. Then, using the method of multiple scales, we assess the poss...

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Bibliographic Details
Published inStructural control and health monitoring Vol. 13; no. 1; pp. 388 - 416
Main Authors Nayfeh, A.H., Arafat, H.N.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.01.2006
Subjects
bifurcation analysis
dynamics
non-linear vibrations
spherical shells
two-to-one internal resonance
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Summary:We investigate the torsionless axisymmetric dynamics of a forced closed spherical shell. The non‐linear equations of motion are formulated using a variational approach and surface analysis. First, we revisit the linear eigenvalue problem. Then, using the method of multiple scales, we assess the possibility of the activation of two‐to‐one internal resonances between the different types of modes. Lastly, we examine the shell's non‐linear responses to an axisymmetric primary‐resonance excitation and analyse their bifurcations. Copyright © 2005 John Wiley & Sons, Ltd.
Bibliography:ark:/67375/WNG-1LF9G1V8-0
ArticleID:STC121
istex:13699C061DA803726C566F4B9FBADF79634E3CFC
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1545-2255
1545-2263
DOI:10.1002/stc.121