Whirling of a forced cantilevered beam with static deflection. II: Superharmonic and subharmonic resonances

Secondary resonances of a slender, elastic, cantilevered beam subjected to a transverse harmonic load are investigated. The effects of nonlinear curvature, nonlinear inertia, viscous damping and static load are included. Cubic terms in the governing equations lead to subharmonic and superharmonic resonances of order three. The static displacement produced by the weight of the beam introduces quadratic terms in the governing equations, which cause subharmonic and superharmonic resonances of order two. Out-of-plane motion is possible in all of these secondary resonances when the principal moments of inertia of the beam cross section are approximately equal.