Dynamics and stability analysis of an axially moving beam in axial flow

2020 ◽  
Vol 15 (1) ◽  
pp. 37-60
Author(s):  
Hao Yan ◽  
Huliang Dai ◽  
Qiao Ni ◽  
Kun Zhou ◽  
Lin Wang
Keyword(s):  
Stability Analysis ◽  
Axial Flow ◽  
Axially Moving Beam ◽  
Moving Beam ◽  
Axially Moving

Vibration and Stability Analysis of Axially Moving Beams with Variable Speed and Axial Force

2014 ◽  
Vol 14 (06) ◽  
pp. 1450015 ◽  
Author(s):  
Bozkurt Burak Özhan
Keyword(s):  
Stability Analysis ◽  
Axial Force ◽  
Multiple Time Scales ◽  
Axially Moving Beam ◽  
Multiple Time ◽  
Vibration Model ◽  
Moving Beam ◽  
Parametric Resonances ◽  
Axially Moving ◽  
Beam Parameters

The well-known vibration model of axially moving beam is considered. Both axial moving speed and axial force are assumed to vary harmonically. The Method of Multiple Time Scales (a perturbation method) is used. The natural vibrations of beam are considered for different values of beam parameters. Resonances are obtained for seven different conditions. Solvability conditions for each resonance case are found analytically. Effects of transport velocity, axial force, rigidity and damping are discussed. Stability analysis are obtained for principal parametric resonances. Stable and unstable regions are obtained regarding velocity and force effects separately and together.

Modeling and Stability Analysis of an Axially Moving Beam With Frictional Contact

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Gottfried Spelsberg-Korspeter ◽  
Oleg N. Kirillov ◽  
Peter Hagedorn
Keyword(s):  
Stability Analysis ◽  
Frictional Contact ◽  
Equations Of Motion ◽  
Axially Moving Beam ◽  
Perturbation Techniques ◽  
Stability Boundaries ◽  
Analytical Approximations ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability

This paper considers a moving beam in frictional contact with pads, making the system susceptible for self-excited vibrations. The equations of motion are derived and a stability analysis is performed using perturbation techniques yielding analytical approximations to the stability boundaries. Special attention is given to the interaction of the beam and the rod equations. The mechanism yielding self-excited vibrations does not only occur in moving beams, but also in other moving continua such as rotating plates, for example.

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.

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