ASYMPTOTIC APPROACH TO SOLUTION FOR NONLINEAR FREQUENCIES OF THIN CYLINDRICAL SHELLS WITH LARGE DEFORMATION

To solve weak-nonlinear vibration problems of cylindrical shells with large deformation, an asymptotic approach to solution for natural frequencies of a thin cylindrical shell with geometric nonlinearities is proposed. Starting with the Donnel's shallow-shell theory, its nonlinear frequency equations with cubic of displacement are obtained. Its displacement and frequency are expanded in a power series of a small nonlinear parameter. The coefficient of the nonlinear item with the same order is equal. It leads to a set of coupled nonlinear algebraic equations about the first order approximations of nonlinear frequencies and initial amplitudes. The frequency equations are orthogonal and uncoupled by Galerkin's method and their secular terms are eliminated. Considering real solutions and no internal resonance between amplitudes of different modes, the perturbation method with small parameter is used and the first order approximations of nonlinear frequencies are finally acquired. Results show that nonlinear frequencies increase with effect of large geometric deformation taken Relationships among linear frequencies, nonlinear frequencies and initial displacements are discussed.