报告主题：On the applicability of perturbation methods in the study of vibrations of axially moving strings and beams
报告人：Wim T. Horssen 教授 （荷兰代尔夫特理工大学）
报告时间：2017年 10月27日（周五）9:00
报告地点：校本部G507
邀请人：白延琴
主办部门：8455新葡萄场网站数学系
报告摘要：In this presentation the transversal vibrations of an axially moving string or beam with constant or time-varying length, time-varying velocity, and/or time-varying tension are studied. By using a multiple timescales perturbation method, asymptotic approximations of the solutions of the formulated initial-boundary value problems are constructed. The applicability of Galerkin’s truncation method and the applicability of the method of characteristic coordinates for these types of problems are discussed. The presence of internal resonances and autoresonances are described in detail. For string-like problems it will be shown how the two timescales perturbation method in combination with the method of characteristic coordinates can be used to construct asymptotic approximations of the solutions on long timescales. Also for these string-like problems it turns out that Galerkin’s truncation method is not applicable to obtain asymptotic results on long timescales.
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