scholarly journals Sub- and super-critical nonlinear dynamics of a harmonically excited axially moving beam

2012 ◽  
Vol 49 (1) ◽  
pp. 227-243 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Hossein A. Kafiabad ◽  
Tyler Reid
Keyword(s):  
Nonlinear Dynamics ◽  
Axially Moving Beam ◽  
Moving Beam ◽  
Axially Moving

Thermo-mechanical nonlinear dynamics of a buckled axially moving beam

2012 ◽  
Vol 83 (1) ◽  
pp. 25-42 ◽  
Author(s):  
Siavash Kazemirad ◽  
Mergen H. Ghayesh ◽  
Marco Amabili
Keyword(s):  
Nonlinear Dynamics ◽  
Axially Moving Beam ◽  
Moving Beam ◽  
Axially Moving

In-plane and out-of-plane nonlinear dynamics of an axially moving beam

2013 ◽  
Vol 54 ◽  
pp. 101-121 ◽  
Author(s):  
Hamed Farokhi ◽  
Mergen H. Ghayesh ◽  
Marco Amabili
Keyword(s):  
Nonlinear Dynamics ◽  
Axially Moving Beam ◽  
Moving Beam ◽  
Out Of Plane ◽  
Axially Moving

Chaotic Dynamics of an Axially Accelerating Viscoelastic Beam in the Supercritical Regime

2014 ◽  
Vol 24 (05) ◽  
pp. 1450062 ◽  
Author(s):  
Hu Ding ◽  
Qiao-Yun Yan ◽  
Jean W. Zu
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Solutions ◽  
Time History ◽  
Axially Moving Beam ◽  
Viscoelastic Beam ◽  
Supercritical Regime ◽  
Axial Acceleration ◽  
Moving Beam ◽  
Galerkin Truncation ◽  
Axially Moving

This paper focuses on the bifurcation and chaos of an axially accelerating viscoelastic beam in the supercritical regime. For the first time, the nonlinear dynamics of the system under consideration are studied via the high-order Galerkin truncation as well as the differential and integral quadrature method (DQM & IQM). The speed of the axially moving beam is assumed to be comprised of a constant mean value along with harmonic fluctuations. The transverse vibrations of the beam are governed by a nonlinear integro-partial-differential equation, which includes the finite axial support rigidity and the longitudinally varying tension due to the axial acceleration. The Galerkin truncation and the DQM & IQM are, respectively, applied to reduce the equation into a set of ordinary differential equations. Furthermore, the time history of the axially moving beam is numerically solved based on the fourth-order Runge–Kutta time discretization. Based on the numerical solutions, the phase portrait, the bifurcation diagrams and the initial value sensitivity are presented to identify the dynamical behaviors. Based on the nonlinear dynamics, the effects of the truncation terms of the Galerkin method, such as 2-term, 4-term, and 6-term, are studied by comparison with DQM & IQM.

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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