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.

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.

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 Nonlinear Controller Design for a Flexible Spacecraft

2020 ◽  
Vol 67 (4) ◽  
pp. 1500-1520
Author(s):  
Jose Luis Redondo Gutiérrez ◽  
Ansgar Heidecker
Keyword(s):  
Controller Design ◽  
Flexible Structures ◽  
Rigid Motion ◽  
Nonlinear Controller ◽  
Assumed Mode Method ◽  
Control Approach ◽  
Mode Method ◽  
Study Case ◽  
Nonlinear Controller Design ◽  
Assumed Mode

AbstractThis paper combines the nonlinear Udwadia-Kalaba control approach with the Assumed Mode Method to model flexible structures and derives an attitude controller for a spacecraft. The study case of this paper is a satellite with four flexible cantilever beams attached to a rigid central hub. Two main topics are covered in this paper. The first one is the formulation of the equation of motion and the second one is the nonlinear controller design. The combination of these two techniques is able to provide a controller that damps the vibration of a flexible structure while achieving the desired rigid-motion state.

Squeal Analysis of a Disc Brake Considering Damping between a Disc and a Pad Lining

2012 ◽  
Vol 157-158 ◽  
pp. 1000-1003
Author(s):  
Ke Wei Zhou ◽  
Cheol Kim ◽  
Min Ok Yun ◽  
Ju Young Kim
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Element Model ◽  
Disc Brake ◽  
Vibration Modes ◽  
Assumed Mode Method ◽  
Frictional Damping ◽  
System Components ◽  
Mode Method ◽  
Assumed Mode

The improved equations of motion for a friction-engaged brake system have been newly derived on the basis of the assumed mode method and frictional damping. The equations of motion with a finite element model were constructed by a set of vibration modes found from FE modal analysis on all system components. Consequently, the modal information of system components are combined with equations of motion derived from the analytical model. Numerical analysis showed the mode which was unstable in an undamped case became stable in a damped case.

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