Proportional distribution pattern and modal principle of tuned viscous mass dampers for multi-degree-of-freedom structures

Abstract

A tuned viscous mass damper (TVMD) is an inerter-based damper that has been adopted in several high-rise buildings in earthquake-prone Japan recently to protect the structures from seismic-induced vibrations. However, as a TVMD contains a mass element, it adds degrees of freedom to the controlled structure, making the system’s eigenmodes complex. Inspired by the Rayleigh damping matrix, this study proposes a mass-proportionally distributed TVMD (MPD-TVMD) system, which enhances the efficiency of TVMD utilization compared to the previously proposed stiffness-proportionally distributed TVMD (SPD-TVMD) system. It is theoretically proven in this study that when the arrangements of the TVMDs are proportional to the stiffness or mass distribution of the primary structure, the equations of motion of a TVMD controlled shear building can be decomposed into the eigenmodes of the uncontrolled structure. This modal principle allows structural engineers to estimate the response of the controlled structure by understanding the modal characteristics of the uncontrolled system, which is highly beneficial for preliminary design decisions and the retrofitting of existing structures. Furthermore, given that the damping properties at each story level are typically adjusted by the number of dampers installed, it is often unrealistic in practical design to maintain strict proportionality in damper distribution. Through numerical examples, this study demonstrates that TVMD systems with realistic distribution patterns that are slightly different from a strictly proportional distribution can still perform as effectively as strictly proportional systems, providing a comprehensive design basis for the application of inerter-based damper in practical engineering.