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.
Rayleigh variational principle and vibrations of prestressed shells
Eremeyev, VA
;
2014-01-01
Abstract
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.
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