Vibration Analysis of Non-linear 6-parameter Prestressed Shells

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.