Dynamic Modeling of an Axially Moving Beam in Rotation: Simulation and Experiment

1991 ◽  
Vol 113 (1) ◽  
pp. 34-40 ◽  
Author(s):  
J. Yuh ◽  
T. Young
Keyword(s):  
Translational Motion ◽  
Robotic Manipulators ◽  
Multivariable Control ◽  
Axially Moving Beam ◽  
Assumed Mode Method ◽  
Moving Beam ◽  
Mode Method ◽  
Simulation And Experiment ◽  
Axially Moving ◽  
Assumed Mode

In this paper, we consider a beam which has a rotational and translational motion. A time-varying partial differential equation and the boundary conditions are derived to describe the lateral deflection of the beam. For multivariable control, an approximated model is also derived by using the assumed mode method. The validity of the approximated model is investigated by the experiment. For different repositional motions, response of the beam is further investigated by computer simulation. Application of the beam to flexible robotic manipulators is discussed with simulation results.

Static Nodes of an Axially Moving String With Time-Varying Supports

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Lei Lu ◽  
Xiao-Dong Yang ◽  
Wei Zhang
Keyword(s):  
Excitation Frequency ◽  
Superposition Method ◽  
Time Varying ◽  
Linear Superposition ◽  
Assumed Mode Method ◽  
Axially Moving String ◽  
Mode Method ◽  
Axially Moving ◽  
Arbitrary Frequency ◽  
Assumed Mode

Abstract By investigating the transverse vibrations of an axially moving string with time-varying supports, the existence and the pattern of static nodes are studied based on the assumed mode method and the linear superposition method. The explicit expressions for the response of the system with five different boundary conditions are illustrated. Traditional excited static strings show nodes when resonance occurs. However, it is found in this study that the static nodes of axially moving strings appear under arbitrary frequency even far away from resonance, if the excitation frequency is higher than the fundamental frequency. The varying nodes and frequencies under different time-varying supports are revealed.

A Method to Improve the Modal Convergence for Structures With External Forcing

1987 ◽  
Vol 54 (4) ◽  
pp. 904-909 ◽  
Author(s):  
Keqin Gu ◽  
Benson H. Tongue
Keyword(s):  
Spatial Distribution ◽  
Free Vibration ◽  
Convergence Rate ◽  
Traditional Approach ◽  
Vibration Modes ◽  
External Forcing ◽  
Slow Convergence ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Assumed Mode

The traditional approach of using free vibration modes in the assumed mode method often leads to an extremely slow convergence rate, especially when discete interactive forces are involved. By introducing a number of forced modes, significant improvements can be achieved. These forced modes are intrinsic to the structure and the spatial distribution of forces. The motion of the structure can be described exactly by these forced modes and a few free vibration modes provided that certain conditions are satisfied. The forced modes can be viewed as an extension of static modes. The development of a forced mode formulation is outlined and a numerical example is presented.

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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