On the optimal design and placement of Tuned-Mass-Damper-Inerter for Multi-Degree-Of-Freedom structures

Even if Tuned-Mass-Damper-Inerter (TMDI) design for Multi-Degree-Of-Freedom (MDOF) structures is a topic largely addressed in the current literature, some aspects still deserving insight emerge from a literature review. The state of the art presented in the paper highlights that Inerter-Vibration-Absorber (IVA) design is typically conducted based on simplified models (e.g. generalized 2-Degree-Of-Freedom (2-DOF) models) or sophisticated ones but a comparison between the two approaches is rarely made. Moreover, the device placement along the structure is not often addressed in the design formulation; nevertheless, a proper location greatly influences the absorber performance and its physical dimensions. The paper aims to be a comprehensive study that investigates in a unique formulation the optimal design together with the optimal placement of a TMDI in a MDOF structure and aims to make a comparison between the use of a 2-DOF model and a complete MDOF model for its optimal design and placement. The overall design methodology and performance evaluation is formulated considering a stationary white noise input. An exemplificative literature case study of a 10-DOF structure is utilized to apply the design procedure, evaluate the performance and make the comparisons. It is demonstrated that a reduced order model is useful for a first estimate of the TMDI design parameters but some, especially the damping coefficient, need improvement adopting more refined models. Structural performance is well cached with reduced order models, especially for those quantities that mainly depend on the first natural mode. An optimal placement, tradeoff between structural performances and absorber physical dimensions, is proposed. TMDI effectiveness is assessed also considering non-stationary input with natural earthquakes and comparisons with conventional and non-conventional Tuned-Mass-Damper (TMD) are conducted.