ISSN:
1573-269X
Keywords:
Cable
;
autoparametric resonance
;
Galerkin procedure
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We discuss solution methods for nonlinear vibrations of cables having small initial sag-to-span ratios. One-to-one internal resonances between the in-plane and out-of-plane modes as well as primary resonances of the in-plane mode are considered. Approximate solutions are obtained by two different approaches. In the first approach, the method of multiple scales is applied directly to the governing partial-differential equations and boundary conditions. In the second approach, the equations are first discretized, and then the method of multiple scales is applied to the resulting ordinary-differential equations. It is shown that treatment of the discretized system is inaccurate compared to direct treatment of the partial-differential system. Discrepancies between the two solutions appear even at the first level of approximation. Stability analyses of the amplitude and phase modulation equations for both methods are also performed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00045007
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