Dynamics of a Flexible Cantilever Beam Carrying a Moving Mass

The motion of a flexible cantilever beam carrying a moving spring-mass system is investigated. The beam is assumed to be an Euler–Bernouli beam. The motion of the system is described by a set of two nonlinear coupled partial differential equations where the coupling terms have to be evaluated at the...

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Bibliographic Details
Published in:Nonlinear dynamics 1998-02, Vol.15 (2), p.137-154
Main Authors: Siddiqui, Sultan A Q, M Farid Golnaraghi, Heppler, Glenn R
Format: Article
Language:English
Subjects:
Cantilever beams
Coupling
Equations of motion
Mass-spring systems
Mathematical analysis
Multiscale analysis
Nonlinear equations
Partial differential equations
Perturbation methods
Ritz method
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Summary:The motion of a flexible cantilever beam carrying a moving spring-mass system is investigated. The beam is assumed to be an Euler–Bernouli beam. The motion of the system is described by a set of two nonlinear coupled partial differential equations where the coupling terms have to be evaluated at the position of the mass. The nonlinearities arise due to the coupling between the mass and the beam. Due to the nonlinearities the system exhibits internal resonance which is investigated in this work. The equations of motion are solved numerically using the Rayleigh–Ritz method and an automatic ODE solver. An approximate solution using the perturbation method of multiple scales is also obtained.
ISSN:0924-090X
1573-269X
DOI:10.1023/A:1008205904691