On the variational analysis of vibrations of prestressed six-parameter shells

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.