Particle swarm optimization of tuned mass dampers

A tuned mass damper (TMD) is a device consisting of small damped spring–mass system attached to a vibrating main system in order to attenuate any undesirable vibrations In this paper, optimum parameters of TMD system attached to a viscously damped single degree-of-freedom main system are derived for various combinations of excitation and response parameters The excitation applied to the main system consists of external force and base acceleration modelled as Gaussian white-noise random process Using numerical searching technique, the optimum damping and tuning frequency ratio of the TMD are obtained for minimization of various mean square responses such as relative displacement, velocity of main mass and force transmitted to the support The optimum parameters of the TMD system and the corresponding response quantities are obtained for different damping ratios of the main system and the mass ratios of the TMD system Explicit formulae for damper damping, tuning frequency and the corresponding minimized response are then derived using curve-fitting technique that can be conveniently used for applications in dynamical systems The error in these expressions is found to be negligible and hence these expressions are convenient for use in damped single degree-of-freedom main system The optimum damping ratio of the TMD is not much influenced by the damping of the main system However, the optimum tuning frequency of TMD is significantly affected by the damping of main system Lastly, a comparison of the optimum damping and tuning frequency of the TMD under filtered white-noise and white-noise excitation is also made Copyright © 2006 John Wiley & Sons, Ltd

Optimum parameters of tuned mass damper for damped main system

Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system

There are many traditional methods to find the optimum parameters of a tuned mass damper (TMD) subject to stationary base excitations It is very difficult to obtain the optimum parameters of a TMD subject to non-stationary base excitations using these traditional optimization techniques In this paper, by applying particle swarm optimization (PSO) algorithm as a novel evolutionary algorithm, the optimum parameters including the optimum mass ratio, damper damping and tuning frequency of the TMD system attached to a viscously damped single-degree-of-freedom main system subject to non-stationary excitation can be obtained when taking either the displacement or the acceleration mean square response, as well as their combination, as the cost function For simplicity of presentation, the non-stationary excitation is modeled by an evolutionary stationary process in the paper By means of three numerical examples for different types of non-stationary ground acceleration models, the results indicate that PSO can be used to find the optimum mass ratio, damper damping and tuning frequency of the non-stationary TMD system, and it is quite easy to be programmed for practical engineering applications

A.G. Thompson

Papers

Optimizing the untuned viscous dynamic vibration absorber with primary system damping: A frequency locus method