|
Xiao Xiwu
Yang Shuzi
Huang Yuying
Department of Mechanics,
Huazhong University of Science
and Technology,
Wuhan 430074, China
|
|
|
1/2 SUBHARMONIC RESONANCE OF
A SHAFT WITH UNSYMMETRICAL
STIFFNESS*
Abstract:
The 1/2 subharmonic resonance of a shaft with unsymmetrical stiffness is studied. By means of the Hamilton’s principle the nonlinear differential equations of motion of the rotating shaft are derived in the rotating rectangular coordinate system. Transforming the equations of motion from rotating coordinate system into stationary coordinate system and introducing a complex variable, the equation of motion in complex variable form is obtained, in which the stiffness coefficient varies periodically with time. It presents a nonlinear oscillation system under parametric excitation. By applying the method of multiple scales (MMS) the averaged equation, the bifurcating response equations and local bifurcating set are obtained. Via the theory of singularity, the stability of constant solutions is analyzed and bifurcating response curves are obtained. This study shows that the rotating shaft has rich bifurcation phenomena.
Key words: Shaft with unsymmetrical stiffness Subharmonic
resonance Stability Bifurcation MMS |