Stability of Nonlinear Two-Frequency Oscillation of Cylindrical Shells

Abstract

The moment scheme of the finite element method and the method of generalized coordinates are used to construct a multi-degree-of-freedom nonlinear model of a cylindrical shell subjected to two-frequency excitations. This model consists of a system of nonlinear differential equations. The incremental method is then used to find the solution of the equation in the frequency domain, while the Poincaré map, spectral analysis, and Floquet's theory are applied to the stability of the solution at every step of the incremental method. Solutions and discussions are presented to substantiate the suggested algorithm. It is shown that similar results are obtained by using the Poincaré map with numerical integration and Floquet's theory with Fourier's expansion. However, Floquet's theory is a lot less time-consuming and it pinpoints more accurately the moment of loss of stability.