Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Shyu, I.-M. K., Mook, D. T., and Plaut, R. H., ‘Whirling of a forced cantilevered beam with static deflection. I: primary resonance’, Nonlinear Dynamics 4, 1993, 227–249.
Shyu, I.-M. K., ‘Forced, nonlinear, planar and nonplanar oscillations of a cantilevered beam including static deflection’, Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shyu, I.M.K., Plaut, R.H. & Mook, D.T. Whirling of a forced cantilevered beam with static deflection. II: Superharmonic and subharmonic resonances. Nonlinear Dyn 4, 337–356 (1993). https://doi.org/10.1007/BF00120670
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00120670