OUT-OF-PLANE VIBRATIONS OF CURVED NON-UNIFORM BEAMS OF CONSTANT RADIUS

✍ Scribed by S.Y. LEE; J.C. CHAO

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 225 KB
• Volume: 238
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2000.3084

✦ Synopsis

The governing di!erential equations for out-of-plane vibrations of curved non-uniform beams of constant radius are derived. Two physical parameters are introduced to simplify the analysis. The explicit relations between the #exural displacement, its "rst three order derivatives and the torsional displacement are derived. With these explicit relations, the two coupled governing characteristic di!erential equations can be decoupled and reduced to a sixth order ordinary di!erential equation with variable coe$cients in the torsional displacement. It is shown that if the material and geometric properties of the beam are in arbitrary polynomial forms of spatial variable, then exact solutions for the out-of-plane vibrations of the beam can be obtained. The derived explicit relations can also be used to reduce the di$culty in experimental measurements. Finally, the in#uence of taper ratio, center angle and arc length on the "rst two natural frequencies of the beams is illustrated.

2000 Academic Press