Non-linear interaction of bending deformations of free-oscillating cylindrical shells

A method is proposed for the calculation of free oscillations of circular cylindrical shells taking into account the non-linear interaction of their bending deformations. Cases are studied in which a shell is characterized by eigenfrequencies, which are in close proximity or multiple frequencies. Based on analysis of the averaged equations, a number of solutions have been constructed. These solutions are used to investigate the particular qualities of the energy exchange and interaction of the modes of the shell. Phase patterns corresponding to interaction of conjugate forms (2-D model) and forms of various wave-forming parameters (4-D model) are studied. The impact of initial conditions on deformation shapes of free multi-mode-oscillating shells is considered.