Nonlinear free vibrations of a cylindrical shell fully filled with a perfect incompressible fluid are studied. The case is examined where two natural frequencies of the shell are close Keywords: cylindrical shell, perfect incompressible fluid, nonlinear vibrations, first integrals, traveling wave Introduction. The nonlinear vibrations of fluid-filled thin shells represented by simple (usually one-degree-of-freedom) models have been studied in sufficient detail (see [1, 2, 7, 9, 12, etc.] for review of such studies). However, such models fail to describe many complex nonlinear phenomena associated with the interaction of two or more different modes of shells filled with a fluid. The coupling of such modes may be a cause of intensive energy exchange among them, in addition to specific ("resonant") conditions. This may result in qualitatively new deformation modes differed from traditional standing waves. These new modes are, in particular, waves traveling in the circumferential direction. We also investigate a superposition of standing and traveling waves, chaotic modes, and other phenomena.The present paper sets forth a method for analysis of the free multimode vibrations with internal resonances of finite-length cylindrical shells filled with a fluid.1. Initial Dynamic Equations. For dynamic equations of a fluid-filled cylindrical shell we use mixed geometrically nonlinear equations of the theory of flexible shallow shells [14]:
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.