Hybrid Inverse Mode Problems for FEM-Shear Models

Abstract

A class of hybrid inverse eigenmode problems is formulated such that a set of stiffnesses of a structure supported by a prescribed shear-type foundation system at an interface is determined for a specified lowest eigenvalue and a specified set of lowest-mode deformation-quantity ratios in the structure. The key point of the hybrid inverse eigenmode formulation is to take full advantage of the dynamic equilibrium of the whole superstructure, including the interface, and to express the lowest-mode interstory-drift components in the foundation system in terms of the specified lowest eigenvalue and the specified lowest-mode deformation quantities in the superstructure. A property on signs of the lowest-mode components is clarified for a general finite-element model supported by a shear-type foundation system. A systematic procedure for determining the stiffnesses of the superstructure is devised. The condition for uniqueness of the stiffnesses is then disclosed. Finally an example of application of this formulation is presented for a finite-element beam model supported by a shear-type foundation system.