DYNAMIC ANALYSIS OF STRUCTURES WITH MULTIPLE TUNED MASS DAMPERS

Roman Lewandowski,Justyna Grzymisławska

doi:10.3846/1392-3730.2009.15.77-86

Roman Lewandowski, Justyna Grzymisławska

Open Access

https://doi.org/10.3846/1392-3730.2009.15.77-86

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Abstract

It is the purpose of this paper to analyse the possibility of reducing the vibrations of frame building structures with the help of multiple tuned mass dampers. Structures exposed to strong winds are considered. Excitation forces, which are functions of wind velocity fluctuations, are treated as random forces. The spectral density functions of wind velocity fluctuations are assumed as proposed by Davenport. The correlation theory of random vibration is used and the root mean squares of displacements and accelerations are determined. Several remarks, concerning the effectiveness of multiple tuned or mass dampers, are formulated from the results of calculation. Santrauka Nagrinėjama galimybė sumažinti stipraus vėjo veikiamų rėminių pastatų konstrukcijų svyravimus, taikant masės slopintuvų sistemą. Vibracijas sukeliančios jėgos, priklausančios nuo vėjo greičio svyravimų, laikomos atsitiktiniais dydžiais. Vėjo greičio svyravimo spektro tankio funkcijos nagrinėjamos Davenport metodu. Atlikus atsitiktinių vibracijų regresinę analizę, nustatytos poslinkių ir pagreičių vidutinės kvadratinės paklaidos. Remiantis skaičiavimo rezultatais, padarytos masės slopintuvų efektyvumo išvados.

Highlights

Mass dampers have been used for reducing the vibrations of structures for many years (McNamara 1977)
For comparison, results for the structure with only one tuned mass damper (TMD), which is tuned to the first vibration mode of structure will be presented
Calculations are made for a structure for which the values of all masses and all stiffness coefficients change by ±10%, but the parameters of tuned mass dampers (TMD) and multiple tuned mass dampers (MTMD) are kept constant

Summary

Introduction

Mass dampers have been used for reducing the vibrations of structures for many years (McNamara 1977). The symbol kij denotes the stiffness coefficient of a damper of the j-th group which is located on the i-th floor (Fig. 2). In the above formulae the symbol cij denotes the damping coefficient of the damper of the j -th group which of the iC~s located matrix on is the the i -th floor

Results

Conclusion