FORCED HARMONIC RESPONSE OF A CONTINUOUS SYSTEM DISPLAYING EIGENVALUEVEERING PHENOMENA

Prior studies of self-adjoint near aa vibratory systems have extensive ly explored the free vibration phenomena associated with veering of ei genvalue loci that depict the dependence of natural frequencies on a s ystem parameter. The present work is an exploration of the effect of s uch phenomena on the response of a nearly-periodic continuum to harmon ic excitation. The focus of the analysis is the prototypical system of a two-span beam with a strong torsional spring at the intermediate pi n support. The results of an exact eigenvalue analysis, not previously disclosed, are used to perform a modal analysis of the steady-state r esponse to a harmonic concentrated force applied to the middle of one span. The modal equations are used to identify situations in which the force response is localized to one span, as well as the degree to whi ch the location and magnitude of the peak displacement display paramet er sensitivity. The effect of hysteretic loss on forced localization I s discussed.