✦ LIBER ✦

IN-PLANE VIBRATION OF CIRCULAR ARCHES WITH VARIABLE CROSS-SECTIONS

✍ Scribed by X. Tong; N. Mrad; B. Tabarrok

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 289 KB
Volume: 212
Category: Article
ISSN: 0022-460X
DOI: 10.1006/jsvi.1997.1441

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✦ Synopsis

Free and forced in-plane vibrations of circular arches with variable cross-sections are investigated. Using the Kirchhoff assumptions for thin beams and taking the neutral axis as inextensible, a closed form solution is obtained for circular arches of uniform cross-section. This exact solution is used for circular arches with stepped cross-sections and is applied to obtain an approximate solution for arches with non-uniform cross-sections. For free vibration, an analytic form of frequency equation is obtained by using the general solution expressed in terms of some initial parameters at one end of the arch; while for forced vibration, the system's response is obtained analytically by solving a set of algebraic equations with only three unknowns. Several examples are presented to illustrate the validity and accuracy of the method.

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