Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On an elastic dissipation model for a cantilevered beam

Authors: W. T. van Horssen and M. A. Zarubinskaya
Journal: Quart. Appl. Math. 61 (2003), 565-573
MSC: Primary 74K10; Secondary 35B35, 35Q72, 74H40
DOI: https://doi.org/10.1090/qam/1999837
MathSciNet review: MR1999837
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Abstract: In this paper we will study an elastic dissipation model for a cantilevered beam. This problem for a cantilevered beam has been formulated by D. L. Russell as an open problem in [1, 2]. To determine the relationship between the damping rates and the frequencies we will use a recently developed, adapted form of the method of separation of variables. It will be shown that the dissipation model for the cantilevered beam will not always generate damping. Moreover, it will be shown that some solutions can become unbounded.

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DOI: https://doi.org/10.1090/qam/1999837
Article copyright: © Copyright 2003 American Mathematical Society

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