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On the Variational Analysis of Vibrations of Prestressed Six-Parameter Shells

  • Holm AltenbachEmail author
  • Victor A. Eremeyev
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 49)

Abstract

We discuss the variational statements of the theory of linear vibrations of prestressed six-parameter shells. Initial or residual stresses can significantly influence buckling and oscillations of thin-walled structures. Within the six-parameter theory of shells a shell is modeled as a deformed material each point of it has six degrees f freedom, that is three translational and three rotational ones. Starting with the governing equations of the six-parameter shell theory the constitutive equations are analyzed. The linearization of the boundary-value problem is realized. After a brief discussion of the eigen-vibrations of the prestressed six-parameter shells the Rayleigh principle is introduced and discussed.

Keywords

Initial Stress Strain Energy Density Rayleigh Quotient Actual Configuration Infinitesimal Deformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Lehrstuhl für Technische Mechanik, Fakultät für MaschinenbauInstitut für Mechanik, Otto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.Department of Applied Mechanics and RoboticsFaculty of Mechanical Engineering and Avionics, Rzeszów University of TechnologyRzeszówPoland

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