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Abstract: We study the vibrations of a hanging thin flexible rod, in which the dominantrestoring force in most of the domain is tension due to the weight of the rod,while bending elasticity plays a small but non-negligible role. We consider alinearized description, which we may reduce to an eigenvalue problem. We solvethe resulting singularly perturbed problem asymptotically up to the firstmodification of the eigenvalue. On the way, we illustrate several importantproblem-solving techniques: modeling, nondimensionalization, scaling, andespecially use of asymptotic series.



Autor: Yossi Farjoun, David G. Schaeffer

Fuente: https://arxiv.org/







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