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COMMENTS ON VIBRATIONS OF NON-UNIFORM BEAMS AND RODS

✍ Scribed by H.P.W. Gottlieb

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 217 KB
Volume: 195
Category: Article
ISSN: 0022-460X
DOI: 10.1006/jsvi.1996.0409

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✦ Synopsis

Abrate [1] has recently produced a neat extension of the transformation trick which yielded a non-uniform rod with uniform rod vibration spectrum for fixed ends, to a case of a non-uniform clamped beam with uniform beam spectrum. The latter, with quartic dependence on spatial co-ordinate for both its moment of inertia and cross-sectional area, is in fact one of several classes of non-uniform beams with the same spectrum as (i.e. isospectral with) a uniform beam which were discovered in reference [2].

For flexural rigidity f(x) and lineal mass density m(x), the result called class (5) in reference [2] may be re-written as

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