THE 1:1 INTERNALLY RESONANT RESPONSE OF A CANTILEVER BEAM ATTACHED TO A ROTATING BODY

✍ Scribed by K.D. Murphy; C.L. Lee

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 270 KB
• Volume: 211
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.1341

✦ Synopsis

Modal coupling in the dynamics of a cantilever beam attached to a rotating body is investigated using a coupled, non-linear three-degree-of-freedom model which includes the effects of centrifugal stiffening. The near-resonant response of two lateral modes (one in-plane and one out-of-plane as defined by the plane of rotation) driven by a periodic out-of-plane excitation is examined for the case in which the natural frequencies of the lateral modes are commensurate in a near one-to-one ratio. The existence and stability of periodic solutions are examined using a second order perturbation analysis. Regions in the system parameter space are identified where single-or multi-mode responses may occur. Typical responses involve Hopf, saddle node and pitchfork bifurcations.