Influence of Proximity Between Modes in the Reduction of Vibrations in Structures Through Absorbers

Abstract

The reductions of vibrations in structures through the addition of passive systems such as absorbers, custom named TMD (Tuned Mass Damper), have been studied by several authors in recent decades. However it has been more stimulated to study the efficiency of these devices by a model that represents the structure by a one degree of freedom mechanical system. This hypothesis is generally valid, since the natural frequency of the mode to be controlled is sufficiently spaced from the adjacent natural frequencies of the structure. Insofar as the degree of structural complexity increases, this assumption becomes less realistic.
The aim of this paper is to investigate the behavior of a structure added by one or more absorbers which has as a dynamical characteristic closely spaced natural frequencies. It was implemented in Fortran a modal analysis program considering non-proportional damping using the IRAM (Implicit restarted Arnoldi Method) to solve the quadratic eigenvalue problem. Analyses were conducted on an aluminum plate modeled by finite element varying the length / width ratio in order to evaluate the interference of modes in the calibration of the absorbers. These tests show that the interaction between the modes produced by absorbers and adjacent modes affect the efficiency of absorption.