×

Determination of the natural frequencies of axially moving beams by the method of multiple scales. (English) Zbl 1174.74319

Summary: The natural frequencies of an axially moving beam are determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method are compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Mote C D, Jr. Dynamic stability of an axially moving band [J]. Journal of Franklin Institute: Engineering and Applied Mathematics, 1968, 285: 329–346. · Zbl 0225.73048
[2] Al-Bedoor B O, Khulief Y A. An approximate analytical solution of beam vibrations during axial motion [J]. Journal of Sound and Vibration, 1996, 192(1): 159–171. · Zbl 0890.73057 · doi:10.1006/jsvi.1996.0181
[3] Wickert J A, Mote C D, Jr. Classical vibration analysis of axially moving continua [J]. Journal of Applied Mechanics, 1990, 57: 738–744. · Zbl 0724.73125 · doi:10.1115/1.2897085
[4] Özkaya E, Öz H R. Determination of natural frequencies and stability regions of axially moving beams using artificial neural networks method [J]. Journal of Sound and Vibration, 2002, 254(4): 782–789. · doi:10.1006/jsvi.2001.3991
[5] Özkaya E, Pakdemirli M. Group theoretic approach to axially accelerating beam problem [J]. Acta Mechanica, 2002, 155(1): 111–123. · doi:10.1007/BF01170843
[6] Öz H R, Pakdemirli M, Özkaya E. Transition behaviour from string to beam for an axially accelerating material [J]. Journal of Sound and Vibration, 1998, 215(3): 571–576. · doi:10.1006/jsvi.1998.1572
[7] Öz H R, Pakdemirli M. Vibrations of an axially moving beam with time-dependent velocity [J]. Journal of Sound and Vibration, 1999, 227(2): 239–257. · doi:10.1006/jsvi.1999.2247
[8] Öz H R, Pakdemirli M, Boyaci H. Nonlinear vibrations and stability of an axially moving beam with time-dependent velocity [J]. International Journal of Non-Linear Mechanics, 2001, 36: 107–115. · Zbl 1342.74077 · doi:10.1016/S0020-7462(99)00090-6
[9] Öz H R. On the vibrations of an axially traveling beam on fixed supports with variable velocity [J]. Journal of Sound and Vibration, 2001, 239(3): 556–564. · doi:10.1006/jsvi.2000.3077
[10] Yang X, Chen L. Free vibrations of axially moving beam on fixed supports [J]. Acta Mechanica Solida Sinica, 2005, 18(3): 242–247.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.