Nonlinear Vibration of Cylindrical Shells

Abstract

The large amplitude vibration of a thin-walled cylindrical shell is analyzed. A perturbation method is used to solve the steady-state forced vibration problem. The simply-supported boundary conditions and the circumferential periodicity condition are satisfied. The resulting solution indicates that in addition to the fundamental mode, the response contains asymmetric modes as well as axisymmetric modes with the frequency twice that of the fundamental mode. Vibrations involving a single driven mode response are investigated. The results indicate that the nonlinear!ty is either softening or hardening depending on the mode. The vibrations involving both a driven mode and a companion mode are also investigated. An experimental investigation is conducted, and the results are in qualitative agreement with the theory. “Nonstationary” response is detected at some frequencies for large amplitude response in which the amplitude drifts from one value to another. Various nonlinear phenomena are observed and comparisons with the theoretical results are made.