A generalized computational model based on modal superposition for dynamic analysis of frame structures with active mass dampers

Abstract The vibration control in civil structures is a primary objective in modern engineering. Among the different vibration control systems, active mass dampers (AMDs) represent a highly effective solution due to their limited invasiveness, optimized use of masses, and thus suitability for both new and existing buildings. When vibrations are detected, an actuator moves the mass in order to generate a force on the structure that is proportional and opposite to the floor velocity: this allows to mitigate oscillations over a broad range of frequencies. Despite their potential, the current design approaches are mostly restricted to regular structures where the cantilever vibration mode is predominant. In this work, a computational framework for the linear dynamic analysis of structures equipped with AMDs is presented. A configuration of AMDs is modelled as a viscous damping having with both translational and rotation contributions and lumped at some floors, leading to non-classical damping conditions. A generalized modal superposition procedure which takes into account phase shift effects is adopted. This allows to evaluate the AMD-induced shear reduction for each vibration mode under a given dynamic action, providing significant insights on the AMD efficiency for superior vibration modes and contributing to their practical implementation in vibration control and seismic protection.