Accession Number : ADA305421

Title :   Higher Order Spectral Investigations of Nonlinear Transverse Vibrations of Circular Rings.

Descriptive Note : Technical rept.

Corporate Author : TEXAS UNIV AT AUSTIN APPLIED RESEARCH LABS

Personal Author(s) : Fox, Douglas J.

PDF Url : ADA305421

Report Date : 19 DEC 1994

Pagination or Media Count : 144

Abstract : The transverse (radial) vibrations of geometrically thin circular rings are experimentally and analytically investigated in order to further understand the order and degree of nonlinearities present. Two important mechanisms have been identified that contribute to the quadratic elements of the nonlinear equations of motion. The first results from the first order nonlinear strain displacement relations interacting with the effect of circumferential periodicity present in a complete ring which gives rise to a double frequency breathing mode. The second mechanism is due to the geometric imperfections present in any manufactured structure which can give rise to a double frequency flexural mode response. These and other nonlinear mechanisms that generate multiple wavenumber responses and interactions among these wavenumbers have been identified. The Galerkin's procedure was used to analytically determine the differential equations of motion. An experimental study has also been conducted on three rings of various thickness to radius ratios. The experimental results question the existence of the nonlinear breathing mode response but confirm, at least qualitatively, the geometric imperfection flexural mode response. The investigation of these nonlinear structural vibrations is enhanced by the use of higher order spectral signal processing, such as bicoherency, which preserves phase information and allows the investigation of frequency interactions and can indicate the presence of nonlinear system effects.

Descriptors :   *VIBRATION, *SHELLS(STRUCTURAL FORMS), *RINGS, THICKNESS, EQUATIONS OF MOTION, STRUCTURAL PROPERTIES, DEFECTS(MATERIALS), QUADRATIC EQUATIONS, DIFFERENTIAL EQUATIONS, THINNESS, NONLINEAR ANALYSIS, RADIUS(MEASURE).

Subject Categories : Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE