Code for symbolic mathematical analysis, simulations and processing of experimental results related to Inerter-based Building Mass Damper

Abstract

The tuned mass damper (TMD) is a classical device interesting for reducing deformations between DOFs without physically connecting them. However, it has a practical limit due to the increase in mass required for improving its performance. A building mass damper (BMD) uses mode coupling to make the upper substructure of a chain-like structure behave as a TMD for the lower substructure, which avoids adding mass to the structure. Unfortunately, near-uniform chain-like structures require isolation of the upper substructure for tuning the BMD, making it impractical for retrofitting existing structures since it is an inseries intervention. This paper proposes and evaluates using an inerter, instead of isolating the upper substructure, to control vibrations through mode coupling in a chain-like structure. From an analytical and numerical study, it was found a significant reduction of lower substructure deformations by implementing solely an inerter and a damper in the upper substructure. The inerter-based approach showed similar performance to the classical BMD with the advantage of being an in-parallel intervention. Therefore, this approach constitutes a practical retrofit to improve the dynamic behavior of existing structures with excessive deformations in a lower substructure whose functionality or esthetics would be compromised if control devices were installed in it.

The Building Mass Damper is a design concept for vibration control of structures where the upper substructure effectively behaves as a Tuned Mass Damper (TMD) for the lower one. Unfortunately, its tuning usually requires softening or partial isolation of the upper substructure; limiting its applicability for retrofitting. The recently proposed Inerter-based Building Mass Damper (IBMD) is an in-parallel intervention on the upper substructure with an inerter and a damper. Thus, the inerter allows correct Tuning, the upper substructure provides the Mass, and the damper adds the Damping. Therefore, a very large mass-ratio TMD is obtained with marginal additional weight and minimal practical impact. In the present work, experimental tests supported by numerical simulations on a small two-story structure model quantitatively confirm the effectiveness of the IBMD. Besides, an innovative compliant mechanism design is introduced for the implementation of the translation-rotational converter that drives the inerter; which has minimal backlash and friction, still allowing large strokes. The experiments involved a frictional damper, which performed comparable to a linear viscous damper considered in the simulations.