Meccanica

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

Vibration Analysis of Non-linear 6-parameter Prestressed Shells

Nonlinear Dynamics and Control of Composites for Smart Engi design

Abstract

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.

Keywords

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

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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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