The Study Of Dynamic Stability Of Shafts Based On Quasi-wavelet Method

Shaft vibration has been one hot research issue. Common shaft vibrations such aslongitudinal, torsional,lateral and coupled vibrations have been investigated deeply, butthe lateral vibration caused by periodic axial force has not been studied by manyresearchers, especially for the parametric resonance or dynamic instability which may becaused by periodic axial force. And the study of the dynamic stability analysis of rotatingshafts has not been very deep. Therefore,it’s necessary to study the parametric resonanceor dynamic instability of shafts deeply. In this paper, the new numerical method—quasi-wavelet method is applied to solve the dynamic stability of beams and rotating shafts, andthe effects of various parameters on the dynamic stability are discussed.This study is mainly divided into two parts: the dynamic stability of non-rotatingshafts (beams)and rotating shafts. First, the dynamic stability of the beams with typicalboundaries are solved by the quasi-wavelet method. And then the dynamic stability of therotating shafts are solved by the quasi-wavelet method, the effects of damping and rotationrate on the dynamic stability are discussed. The detail works in this thesis are as follows:(1) The dynamic stability of Enler beams with typical rigid and elastic boundaryconditions is solved by the quasi-wavelet algorithm.The comparisons with existinganalytical solutions verify the feasibility and effectiveness of quasi-wavelet to this class ofproblem. And effects of constant term in the periodic axial force, viscous damping andmaterial damping, longitudinal resonance on the dynamic instability regions are discussed.(2) The dynamic stability of Timoshenko beams with rotary inertia and sheardeformations effects is solved by the improved quasi-wavelet algorithm. The effects ofrotary inertia and shear deformations effects on the dynamic instability regions arediscussed. The numerical results agree well with the existing analytical solutions.(3) The dynamic stability of rotating shafts is solved by the quasi-wavelet algorithm,the effects of different rotation rates on the dynamic stability of rotating shafts withoutdamping and with damping are discussed. It is found that the dynamic instability region ofrotating shafts without damping does not change with rotation rate when the rate is lowerthan the natural frequency of the first order mode; while the dynamic instability region with damping becomes large with the rotation rate increasing. The numerical results agreewell with the approximate solutions by Floquet method.(4) The dynamic stability of rotating ship shafts is solved by the quasi-waveletalgorithm, the effects of the number of blades of the propeller on the dynamic stability ofrotating ship shafts without damping and with damping are discussed. It is found that thedynamic instability region of rotating ship shafts without damping does not change withthe number of blades; while the dynamic instability region with damping becomes smallwith the number of blades increasing. The numerical results agree well with theapproximate solutions by Floquet method.