Asymptotic Separation of the Spectrum in Notched Rods

Abstract

Theoretical analysis of the axial vibration of slender notched rods via localized compliance models indicates that when there are N notches, the higher part of the spectrum splits in N + 1 branches. Although the separation property is supposed to be valid only in the asymptotic sense, in this paper the authors show that there are cases in which it can be observed and quite accurately measured experimentally, even for relatively low frequencies.