Analytical and Experimental Investigation of the Damping Matrix in Shear Building Models

Abstract

In this thesis, we present a study conducted on investigating the nature of damping matrix associated with multi degree of freedom simple shear building models. The various conventional methods of creating damping matrices in structures are summarized and numerical examples are used to illustrate the inconsistencies among them. Numerical examples are also used to illustrate the significance of non-zero off diagonal terms in the transformed damping matrix obtained after pre and post multiplication with mode shape matrix, i.e. the significance of non-classical nature of damping matrix in certain cases. The analytical study is followed by the description of a laboratory experiment that is developed to evaluate the validity of analytical results. The results from experimental studies of simple 2-DOF and 3-DOF shear building models, both with and without supplemental damping devices, are presented to validate the inconsistencies associated with the conventional methods of creating damping matrices in structures. It is also shown that the incorrect formulation of damping matrix results in highly incorrect responses. Several formulations for damping matrices are then proposed and their validity is evaluated by comparison with experimental results.