Nonlinear dynamic response of rotating circular cylindrical shells with precession of vibrating shape—Part I: Numerical solution

The nonlinear dynamic response of a cantilever rotating circular cylindrical shell subjected to a harmonic excitation about one of the lowest natural frequency, corresponding to mode (m=1, n=6),where m indicates the number of axial half-waves and n indicates the number of circumferential waves, is investigated by using numerical method in this paper. The factor of precession of vibrating shape ? is obtained, with damping accounted for. The equation of motion is derived by using the Donnell’s nonlinear shallow-shell theory, and is general in the sense that it includes damping, Coriolis force and large-amplitude shell motion effects. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. Three different mode expansions are studied for finding the proper one which is more contracted and accurate to investigate the principal mode (i.e., m=1, n=6) response. From the present investigation, it can be found that for principal mode resonant response, there are two traveling waves with different linear frequencies due to the effect of precession of vibrating shape of rotating circular cylindrical shells; the effects of additional modes n and k (multiples of frequency) on the principal mode resonant response are insignificant compared with an additional mode m, showing that it is better to adopt two neighboring axial modes to study the principal resonant response of the system.