The Nonlinear Vibration of Axially Moving Beam Impacted by High-Speed Moving Load

2007 ◽  
pp. 402-402
Author(s):  
Baoquan Guo ◽  
Shilin Xie ◽  
Xinong Zhang
Keyword(s):  
Nonlinear Vibration ◽  
High Speed ◽  
Moving Load ◽  
Axially Moving Beam ◽  
Moving Beam ◽  
Axially Moving

scholarly journals Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Bamadev Sahoo ◽  
L. N. Panda ◽  
G. Pohit
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Time History ◽  
Mean Value ◽  
Phase Portraits ◽  
Axially Moving Beam ◽  
Internal Resonances ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability

The nonlinear vibration of a travelling beam subjected to principal parametric resonance in presence of internal resonance is investigated. The beam velocity is assumed to be comprised of a constant mean value along with a harmonically varying component. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times that of first mode; a three-to-one internal resonance is possible. The method of multiple scales (MMS) is directly applied to the governing nonlinear equations and the associated boundary conditions. The nonlinear steady state response along with the stability and bifurcation of the beam is investigated. The system exhibits pitchfork, Hopf, and saddle node bifurcations under different control parameters. The dynamic solutions in the periodic, quasiperiodic, and chaotic forms are captured with the help of time history, phase portraits, and Poincare maps showing the influence of internal resonance.

On the dynamics of an axially moving beam

1974 ◽  
Vol 297 (3) ◽  
pp. 201-220 ◽  
Author(s):  
B. Tabarrok ◽  
C.M. Leech ◽  
Y.I. Kim
Keyword(s):  
Axially Moving Beam ◽  
Moving Beam ◽  
Axially Moving
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