Rayleigh variational principle and vibrations of prestressed shells

Within the framework of the nonlinear six-parameter theory of shells we discuss the influence of initial (residual) stresses on eigen-frequencies of shells. For a linearized boundary-value problems we formulate the Rayleigh variational principle which gives the possibility to estimate the spectrum of eigen-frequencies of a 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 stresses