Routes to Chaos Exhibited by Closed Flexible Cylindrical Shells

Abstract

Complex vibrations of closed cylindrical shells of circular cross section and finite length subjected to nonuniform sign-changeable external load in the frame of classical nonlinear theory are studied. A transition from partial differential equations to ordinary differential equations (Cauchy problem) is carried out using the higher order Bubnov–Galerkin’s approach and Fourier’s representation. On the other hand, the Cauchy problem is solved using the fourth-order Runge–Kutta method. Results are analyzed owing to the application of nonlinear dynamics and qualitative theory of differential equations. The present work is devoted to the analysis of influence of the system dynamics of the following parameters: length of pressure width φ0, relative linear shell dimension λ=L∕R, and frequency ωp and amplitude q0 of external transversal load. Some new scenarios of vibrations of closed cylindrical shells exhibiting a transition from harmonic to chaotic vibrations are illustrated and studied.