On Travelling Wave Modes of Axially Moving String and Beam

The traditional vibrational standing-wave modes of beams and strings show static overall contour with finite number of fixed nodes. The travelling wave modes are investigated in this study of axially moving string and beam although the solutions have been obtained in the literature. The travelling wave modes show time-varying contour instead of static contour. In the model of an axially moving string, only backward travelling wave modes are found and verified by experiments. Although there are n − 1 fixed nodes in the nth order mode, similar to the vibration of traditional static strings, the presence of travelling wave phenomenon is still spotted between any two adjacent nodes. In contrast to the stationary nodes of string modes, the occurrence of galloping nodes of axially moving beams is discovered: the nodes oscillate periodically during modal motions. Both forward and backward travelling wave phenomena are detected for the axially moving beam case. It is found that the ranges of forward travelling wave modes increase with the axially moving speed. It is also concluded that backward travelling wave modes can transform to the forward travelling wave modes as the transport speed surpasses the buckling critical speed.

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Vibration Localization in Dual-Span, Axially Moving Beams: Formulation and Results

14th Biennial Conference on Mechanical Vibration and Noise: Structural Dynamics of Large Scale and Complex Systems ◽

10.1115/detc1993-0171 ◽

1993 ◽

Author(s):

A. A. N. Al-jawi ◽

Christophe Pierre ◽

A. G. Ulsoy

Keyword(s):

Axially Moving Beam ◽

Mode Localization ◽

Vibration Localization ◽

Natural Modes ◽

Axial Tension ◽

Localization Phenomenon ◽

Moving Beam ◽

Solution Methods ◽

Axially Moving Beams ◽

Axially Moving

Abstract An investigation of the vibration localization phenomenon in dual-span, axially moving beams is presented. The effects of a tension difference among the spans, also referred to as disorder, on the natural modes of free vibration are studied in terms of interspan coupling and transport speed. The equations governing the transverse vibration of the two-span, axially moving beam are derived through Hamilton’s principle and solution methods are developed. Results demonstrate that normal mode localization indeed occurs for both stationary and translating disordered two-span beams, especially for small interspan coupling. The occurrence of localization is characterized by a peak deflection much greater in one span than in the other. In the stationary disordered case, localization becomes more pronounced as interspan coupling decreases, i.e., as the span axial tension increases. In the axially moving disordered case, the transport speed has a significant influence on localization, and generally speaking localization becomes stronger with increasing speed. For a moving beam with identical spans, the two loci of each pair of natural frequencies may exhibit one or more crossing(s) (depending on the value of tension) when plotted against the axial transport speed. These crossings become veerings when the beam is disordered, and localization is strongest at those speeds where the eigenvalue veerings occur.

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Vibration of an axially moving beam with a tip mass

Mechanics Research Communications ◽

10.1016/0093-6413(93)90028-m ◽

1993 ◽

Vol 20 (5) ◽

pp. 391-397 ◽

Cited By ~ 2

Author(s):

Heow-Pueh Lee

Keyword(s):

Axially Moving Beam ◽

Moving Beam ◽

Axially Moving ◽

Tip Mass

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VIBRATIONS OF AN AXIALLY MOVING BEAM WITH TIME-DEPENDENT VELOCITY

Journal of Sound and Vibration ◽

10.1006/jsvi.1999.2247 ◽

1999 ◽

Vol 227 (2) ◽

pp. 239-257 ◽

Cited By ~ 186

Author(s):

H.R. ÖZ ◽

M. PAKDEMİRLİ

Keyword(s):

Time Dependent ◽

Axially Moving Beam ◽

Moving Beam ◽

Axially Moving

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Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

Modelling and Simulation in Engineering ◽

10.1155/2013/919517 ◽

2013 ◽

Vol 2013 ◽

pp. 1-18 ◽

Cited By ~ 5

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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