| Summary: | 碩士 === 國立臺灣科技大學 === 工程技術研究所 === 81 === This study investigates the parametric instability of a can-
tilever pret- wisted orthotropic beam under three conditions,
r- espectively. The first condition is that the beam is applied
al- ong its longitudinal axis by a time-dependent end axial
force which contains a steady-state part and a small,
periodically fl- uctuating component. The second condition is
that the beam rota- tes around its longitudinal axis with a
constant speed and is aslo subjected to the first condition.
The third condition is that the beam, which is aslo
subjected a constant axial force , rotates around its
longitudinal axis with a time-dependent speed which contains a
steady-state part and a small,periodically flu- ctating
component. This structural element can be used to model fluted
cutting tools such as the teist drill bit and the end
milling cutter, etc.. Using the Euler beam theory and
IIamiltion's principle, the present study first derives the
equation of motion which governs the lateral vibration of a
spinning pretwisted orthotropic beam. The rotary inertia,
structual damping and end axial force are included. Then,
the Galerkin method is applied to obtain the as- sociated
finite element equation of motion. Before solving it, the
resulting finite element equation of motion is partially
decoupled by using a suitable modal analysis procedure.
Finally this set of simultaneous differential equation is
solved by the method of multiple scales, yielding the system
response and exp- ressions for the boundaries of the unstable
regions. Numerical results are presented to demonstrate the
effects of various parameters,such as cross-sectional thick-to-
width ratio, prewist angle,spinning speed and end axial force,
on the bounda- ries of unstable regions of the present problem.
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