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

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


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.


Initial Stress Strain Energy Density Rayleigh Quotient Actual Configuration Infinitesimal Deformation 
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© 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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