Stability, bifurcation and chaos of closed flexible cylindrical shells

Abstract

Complex vibrations of closed cylindrical shells of infinite length and circular cross-section subjected to transversal local load in the frame of the classical non-linear theories are studied. A transition from partial differential equations (PDEs) to ordinary differential equations (ODEs) is carried out using a higher-order Bubnov–Galerkin approach and Fourier representation. On the other hand, the Cauchy problem is solved using the fourth-order Runge–Kutta method. In the first part of this work, static problems of the theory of closed cylindrical shells are studied. Reliability of the obtained results is verified by comparing them with the results taken from literature. The second part is devoted to the analysis of stability, bifurcation and chaos of closed cylindrical shells. In particular, an influence of sign-changeable external pressure and the control parameters such as magnitude of pressure measured by ϕ 0, relative linear shell dimension λ= L/ R, frequency ω p and amplitude q 0 of external transversal load, on the shell's non-linear dynamics is studied.