FREE VIBRATIONS OF ELLIPTICAL RINGS WITH CIRCUMFERENTIALLY VARIABLE THICKNESS

✍ Scribed by R.S. HWANG; C.H.J. FOX; S. MCWILLIAM

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 177 KB
• Volume: 228
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2421

✦ Synopsis

This paper deals with the in-plane free vibration of rings with a nominally elliptical centreline. Results are presented for rings of constant axial length that have a rectangular cross-section, the radial thickness of which is constant or has a simple, analytically de"ned circumferential variation. Additionally, and for the "rst time, the e!ects of small variations in in-plane pro"le, such as those arising in practical rings due to manufacturing tolerances, are considered. The problem is tackled using an approach in which the true middle surface is determined numerically from the outer and inner surface pro"les, which can be de"ned either by exact analytical expressions or in a more general way using Fourier series. The Rayleigh}Ritz method is used to obtain the natural frequencies and mode shapes. Results are presented for a range of cases, including some that have previously been studied by other authors and some that have not. The e!ects on frequency splitting due to pro"le variations and the aspect ratio of the ellipse are emphasized. Results obtained using the developed numerical approach show excellent agreement with "nite element predictions.