Fixed-base poles and eigenvectors from transmission zeros

Abstract

An approach to identify building eigenproperties for fixed base conditions, applicable to cases where measurements are from seismic excitation is presented. The approach extracts the fixed base poles from a state space realization where the input is the free field and the output is the base motion, which is assumed rigid. The formulation holds for arbitrary damping distributions and provides, in addition to the poles, the fixed base eigenvectors at any point where the structural response is measured. The approach is built on the fact that the transmission zeros of the foundation transfer matrix can be extracted from measurements and that these zeros are the poles of the fixed base system. Under the premise of linearity and finite dimensionality the method is exact when the map from the free field to the foundation coordinates is itself exact. In practice modal truncation is inevitable and approximation from this source is mitigated using a pseudo-static correction that for a half-space proves a function of the foundation geometry but not of the shear wave velocity. Performance of the approach is examined in simulations and an application in a real structure is illustrated.