ON THE MODE SPLITTING OF DEGENERATE MECHANICAL SYSTEMS CONTAINING CRACKS

This paper presents sufficient conditions governing mode splitting in a two-dimensional, degenerate, mechanical system whose eigensolutions satisfy the Helmholtz equation. When cracks are introduced into such s ystems, a pair of repeated vibration modes may remain repeated or beco me distinct (termed split modes) depending on the location and geometr y of the cracks. Two types of split modes can occur. Split modes of th e first kind are a pair of split modes in which one mode undergoes a f requency shift but the other does not. In contrast, split modes of the second kind are a pair of split modes in which both modes undergo fre quency shifts. A sufficient condition for split modes of the first kin d is derived through an orthogonal transformation of repeated eigenmod es of the perfect system. Sufficient conditions for repeated modes and split modes of the second kind are derived through an asymptotic anal ysis. Numerical examples on square and circular domains illustrate the analytical predictions on mode splitting.