THE INFLUENCE OF INTERNAL RESONANCES ON THE DYNAMICS OF FLUIDFILLED CYLINDRICAL SHELLS

Abstract

Cylindrical shells exhibit a dense frequency spectrum, especially near the lowest frequency range. In addition, due to the circumferential symmetry, frequencies occur in pairs. So, in the vicinity of the lowest natural frequencies, several equal or nearly equal frequencies may occur, leading to a complex dynamic behavior. The aim of this paper is to investigate the influence of these internal resonances on the nonlinear dynamics and instabilities of axially loaded fluid-filled cylindrical shells. For this, a modal solution that takes into account the modal interaction among the relevant modes and satisfies the boundary and continuity condi- tions of the shell is derived. The shell is modeled using the Donnell nonlinear shallow shell theory and the discretized equations of motion are obtained by applying the Galerkin method. The shell is assumed to be completely filled with a dense fluid. The fluid is assumed to be in- compressible and non-viscous and its irrotational motion is described by a velocity potential that satisfies the Laplace equation and relevant boundary and continuity conditions. Solving numerically the governing equations of motion, a detailed parametric analysis is conducted to clarify the influence of the internal resonances on the bifurcations, stability boundaries and nonlinear vibration modes.