Modal mass estimation from ambient vibrations measurement: A method for civil buildings

Abstract

A new method for estimating the modal mass ratios of buildings from unscaled mode shapes identified from ambient vibrations is presented. The method is based on the Multi Rigid Polygons (MRP) model in which each floor of the building is ideally divided in several non-deformable polygons that move independent of each other. The whole mass of the building is concentrated in the centroid of the polygons and the experimental mode shapes are expressed in term of rigid translations and of rotations. In this way, the mass matrix of the building can be easily computed on the basis of simple information about the geometry and the materials of the structure. The modal mass ratios can be then obtained through the classical equation of structural dynamics. Ambient vibrations measurement must be performed according to this MRP models, using at least two biaxial accelerometers per polygon. After a brief illustration of the theoretical background of the method, numerical validations are presented analysing the method sensitivity for possible different source of errors. Quality indexes are defined for evaluating the approximation of the modal mass ratios obtained from a certain MRP model. The capability of the proposed model to be applied to real buildings is illustrated through two experimental applications. In the first one, a geometrically irregular reinforced concrete building is considered, using a calibrated Finite Element Model for validating the results of the method. The second application refers to a historical monumental masonry building, with a more complex geometry and with less information available. In both cases, MRP models with a different number of rigid polygons per floor are compared.