Mathematical structure of modal interactions in a spinning disk restrained by multiple stationary load systems
Journal
Journal of the Chinese Institute of Engineers, Series A/Chung-kuo Kung Ch'eng Hsuch K'an
Journal Volume
19
Journal Issue
6
Pages
681-688
Date Issued
1996
Author(s)
Abstract
Abstract Modal interaction usually occurs in a spinning disk under stationary load systems when two modes are almost degenerate. This paper investigates the mathematical structure of various types of modal interactions analytically by a two‐mode eigenfunction expansion technique. Emphasis is given to the effect of the number of load systems on the eigenvalues of the coupled system. Generally speaking, the frequency loci may merge together (when one of these two modes is a reflected wave) or veer away (when both modes are non‐reflected) when the difference between the numbers of nodal diameters of these two modes is equal to a multiple of the number of the stationary load systems. Otherwise, the natural frequency loci simply cross each other and no instability is induced. In applying these rules the number of nodal diameters of a forward or a reflected wave is considered as negative.
Type
journal article