Nonlinear Dynamics and Bifurcations of an Axially Moving Beam

1999 ◽  
Vol 122 (1) ◽  
pp. 21-30 ◽  
Author(s):  
F. Pellicano ◽  
F. Vestroni
Keyword(s):  
High Dimensional ◽  
Axially Moving Beam ◽  
Dimensional System ◽  
Global Dynamics ◽  
Dimensional Phase Space ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability ◽  
The Galerkin Method ◽  
Sample Case

The present paper analyzes the dynamic behavior of a simply supported beam subjected to an axial transport of mass. The Galerkin method is used to discretize the problem: a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities is obtained. The system is studied in the sub and super-critical speed ranges with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning the convergence of the series expansion, linear subcritical behavior, bifurcation analysis and stability, and direct simulation of global postcritical dynamics. A homoclinic orbit is found in a high dimensional phase space and its stability and collapse are studied. [S0739-3717(00)00501-8]

Post-Critical Dynamics of an Axially Moving Beam

1997 ◽  
Author(s):  
Fabrizio Vestroni ◽  
Francesco Pellicano
Keyword(s):  
Dynamic Behaviour ◽  
High Dimensional ◽  
Axially Moving Beam ◽  
Dimensional System ◽  
Global Dynamics ◽  
Direct Simulation ◽  
Moving Beam ◽  
Axially Moving ◽  
The Galerkin Method ◽  
Sample Case

Abstract In the present paper, the dynamic behaviour of a beam subjected to an axial transport of mass is analyzed. The Galerkin method has been used to discretize the problem; a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities is obtained. The system is studied in the sub and supercritical speed ranges with emphasis on the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning linear subcritical behaviour, static bifurcation analysis including linear stability and direct simulation of global postcritical dynamics.

Post-Critical Response of an Axially Moving Beam

1999 ◽  
Author(s):  
Francesco Pellicano ◽  
Fabrizio Vestroni
Keyword(s):  
Axially Moving Beam ◽  
Dimensional System ◽  
Global Dynamics ◽  
Wide Range ◽  
Moving Beam ◽  
Speed Range ◽  
Traveling Beam ◽  
Axially Moving ◽  
The Stability ◽  
The Galerkin Method

Abstract In this paper the dynamic response of a simply supported traveling beam, subjected to a pointwise transversal load, is investigated. The motion is described by means of a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities obtained through the Galerkin method. The system is studied in the super-critical speed range with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning bifurcation analysis and stability, and direct simulations of global postcritical dynamics. In the supercritical speed range a regular motion around a bifurcated equilibrium position becomes chaotic for particular values of frequency and force. The bifurcation diagram for varying force intensity is shown, it can be noticed that a chaotic motion occurs in a wide range of the forcing parameter, co-existing with a 3T periodic solution in a limited window.

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.

scholarly journals Thermal Effects on Nonlinear Vibrations of an Axially Moving Beam with an Intermediate Spring-Mass Support

2013 ◽  
Vol 20 (3) ◽  
pp. 385-399 ◽  
Author(s):  
Siavash Kazemirad ◽  
Mergen H. Ghayesh ◽  
Marco Amabili
Keyword(s):  
Thermal Loading ◽  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Time Integration ◽  
Harmonic Excitation ◽  
Axially Moving Beam ◽  
Moving Beam ◽  
Axially Moving ◽  
The Galerkin Method ◽  
Continuation Technique

The thermo-mechanical nonlinear vibrations and stability of a hinged-hinged axially moving beam, additionally supported by a nonlinear spring-mass support are examined via two numerical techniques. The system is subjected to a transverse harmonic excitation force as well as a thermal loading. Hamilton's principle is employed to derive the equations of motion; it is discretized into a multi-degree-freedom system by means of the Galerkin method. The steady state resonant response of the system for both cases with and without an internal resonance between the first two modes is examined via the pseudo-arclength continuation technique. In the second method, direct time integration is employed to construct bifurcation diagrams of Poincaré maps of the system.

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.

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