Design formulas for tuned mass dampers based on A perturbation technique

Abstract

SUMMARYModal properties of tuned mass damper (TMDtstructure two-degree-of-freedom (2DOF) linear systems are studied employing a perturbation technique. Using the perturbation solutions, formulas relevant to designing the T M D for various types of loading are obtained; they are expressed as a function of mass ratio, tuning ratio, damping ratio of the T M D and damping ratio of the structure. Equivalent additional dampings of the structure due to the T M D are derived for random and harmonic forces. Matched expressions of equivalent damping, which are valid for detuned, i.e. non-optimal, conditions are also presented. The stability boundary of TMD-structure systems subject to linear self-excited forces is derived in a closed form. Using the perturbation solutions, procedures for optimizing the T M D parameters for various types of loading are explained and the optimal values are derived. The formulas obtained in this study can be used with good accuracy for mass ratios less than 0.02.

Simple and double Hopf bifurcations in aeroelastic oscillators with tuned mass dampers

“…Many authors have proposed different methods to design the spring-viscous connection of the added mass to the system for reaching a suitable tuning to the frequency of an assigned mode, see e.g. [8,9]. The effects of the others modes of the system have recently been investigated either in forced oscillations, [10], than in self-excited oscillations [11].…”

Dynamic Behavior of Steel Frames With Tuned Mass Dampers

“…Although the main types of structural control are active and passive systems, usage of the passive system is more common due to economic and physical conditions [11].…”

Galloping Control for Iced Conductors using Tuned Mass Dampers with time-delayed feedbacks

“…The TMD is widely used in vibration control of building, bridge and mechanical system. Previous studies are mainly devoted to design the spring-viscous connection of the added mass to the system for reaching a suitable tuning to the frequency of an assigned mode [7][8][9][10][11]. However, the TMD with time-delayed feedbacks may be another way to increase the energy dissipating of system and also has a better effect.…”