Seismic response of combined primary-secondary structures with the component-mode synthesis method

This paper deals with the dynamic analysis of primary-secondary combined systems. The problem of selecting the vibrational modes to be retained in analysis is first addressed, for the case of secondary substructures which may possess numerous lowfrequency modes with negligible mass, and a dynamic mode acceleration method (DyMAM) is adopted in view of the application for seismic analysis. The influence of various approaches to build the viscous damping matrix of the primary-secondary assembly is then investigated, and a novel technique based on modal damping superposition is proposed. The results of a parametric study for a representative staircase system multi-connected to a two-dimensional multi-storey frame reveal that the DyMAM correction is capable of increasing the response accuracy with a reduced number of modes compared to the classical MAM (modal acceleration method). Furthermore, a new technique is proposed for assembling the damping matrix, which is shown to be a convenient alternative for modelling the dissipative forces in composite systems. Indeed, while mass and stiffness matrices can unambiguously be defined, various assumptions can be made for the damping matrix, inducing considerable variation in the predicted seismic response.