A HYBRID INVERSE MODE PROBLEM FOR FIXED-FIXED MASS-SPRING MODELS

A hybrid inverse mode problem is formulated for a fixed-fixed mass-spr ing model. A problem of eigenvalue analysis and its inverse problem ar e combined in this hybrid inverse mode formulation. It is shown if all the masses and the mid-span stiffnesses of the model are prescribed, then. the stiffnesses of the left and right spans (side-spans) can be found for a specified lowest eigenvalue and a specified set of lowest- mode drifts in the side-spans. Sufficient conditions are introduced an d proved for a specified eigenvalue and a specified set of drifts in t he side-spans to provide positive stiffnesses of the side-spans and to be those in the lowest eigenvibration. A set of solution stiffnesses in the side-spans is derived uniquely in closed form.