Dynamics of an Elastic Cable Carrying a Moving Mass Particle |
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| Authors: | Al-Qassab M Nair S O'Leary J |
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| Institution: | (1) Mechanical Engineering Department, University of Bahrain, P.O. Box 32038, Manama, Kingdom of Bahrain;(2) Mechanical, Materials and Aerospace Engineering Department, Illinois Institute of Technology, 10 West 32nd St., Chicago, IL, 60616, U.S.A;(3) Civil and Architectural Engineering Department, Illinois Institute of Technology, 3300 South Federal Street, Chicago, IL, 60616, U.S.A |
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| Abstract: | The dynamic behavior of an elastic catenary cable due to a moving mass alongits length is investigated. The equations of motions are derived using theHamilton's principle for general supports that include the horizontal andinclined cables with small and large sags and for variable velocity of themoving mass. Those equations of motions are in general nonlinear partialdifferential equations due to the initial curvature of the cable. Theequations are also complex due to the presence of three different types ofaccelerations of the moving mass. Those are the normal, Coriolis andcentrifugal accelerations. Therefore, we used the Galerkin procedure withsine function (Fourier representation) and anti-derivative functions of thecompactly supported wavelets as trial basis and used direct integrationmethods to integrate the discretized equations of motions. Newton–Raphsonmethod is used for iterations. Several examples are studied and the resultsas obtained by Fourier and wavelet representations are compared. Because ofthe localization feature, wavelets are proven to minimize the spuriousoscillations specially those appearing in the cable tension. |
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| Keywords: | elastic cable cable dynamics moving mass wavelets |
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