, Volume 49, Issue 8, pp 1751–1761 | Cite as

Vibration Analysis of Non-linear 6-parameter Prestressed Shells

  • Holm Altenbach
  • Victor A. EremeyevEmail author
Nonlinear Dynamics and Control of Composites for Smart Engi design


Within the framework of the nonlinear six-parameter shell theory we discuss the influence of initial (residual) stresses on the eigen-frequencies. We derive the linearized boundary-value problems and formulate the Rayleigh variational principle which gives the possibility to estimate the eigen-frequencies of the prestressed shell. The Rayleigh quotient of the shell with initial stresses is represented as a sum of two terms. The first term depends on elastic moduli of the shell while the second one is determined by initial stress and couple stress tensors acting on the shell.


Residual stress Linear vibration 6-parameter shell Variational method Rayleigh principle 



The authors acknowledge funding from the E.U. FP7 Programme FP7-REGPOT-2009-1 under grant agreement no:245479. The second author (V.A.E.) acknowledges support by the German Research Foundation (grant AL341/33-1) and by the Russian Foundation of Basic Research (grant 12-01-00038).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Otto-von-Guericke-University MagdeburgMagdeburgGermany
  2. 2.South Scientific Centre of RASci & South Federal UniversityRostov on DonRussia

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