Hybrid Inverse Eigenmode Problem for a Shear Building Supporting a Finite Element Subassemblage

Abstract

A theory for a new hybrid inverse eigenmode problem is developed such that a set of story stiffnesses of a shear building model supporting a given finite element (FE) subassemblage is found for a specified lowest eigenvalue of the combined system and a specified set of lowest-mode interstory drifts in the shear building model. It is shown that if the lowest eigenvalue is specified so as to be smaller than that of the corresponding rigidly supported model, then the lowest-mode displacements in the FE subassemblage can be expressed uniquely in terms of the given parameters. For a model in which all the lowest-mode horizontal displacements in the FE subassemblage have the same sign as that of the lowest-mode horizontal displacement of the interface, it is shown that if all the lowest-mode interstory drifts in the shear building model have the same sign, then the positive definiteness of the interstory stiffnesses of the shear building model is guaranteed. These facts are demonstrated to be valid through a two-story shear building model supporting a two-story shear system with given stiffnesses. It is further shown that the present theory for a hybrid inverse eigenmode problem can be applied for strengthening or retrofitting a building frame using a base-isolation system.