Abstract: The frequency veering and mode shape interaction properties of the first-order approximation coupling model with rigid-flexible coupling effect of a rotating cantilever beam is studied. Based on the accurate description of non-linear deformation of the flexible beam, the first-order approximation coupling model with the dynamic stiffening terms are derived from Hamilton theory and Rayleigh-Ritz assumed mode method, taking the second-order coupling quantity of axial displacement caused by transverse displacement of the beam into account. The coupling model is transformed into dimensionless form in which dimensionless parameters are identified. The natural frequencies and mode shapes of the rotating cantilever beam with coupling effect are computed by using state space method. The results obtained in the investigation indicate that the influence of the coupling effect on the natural frequencies of the rotating cantilever beam becomes larger as the rotating speed increases. It is shown that besides the frequency veering phenomenon between adjacent two-mode accompanied by mode shape interaction, the transitive frequency veerings among multi-mode accompanied by mode shape shift of a rotating cantilever beam with coupling effect are found and must be further researched deeply. The multi-frequency veerings between an adjacent two-mode are also found.

Key words: frequency veering, mode shape interaction, rigid-flexible coupling, rotating cantilever beam