Perturbation analysis of a Multi-Degree-Of-Freedom system equipped with only one tuned mass damper

This paper develops a simple mathematical model for the analysis of
a 2-dof modal model equipped with a tuned mass damper. The nal aim of this
formulation is to develop a simple design procedure to assess the in
uence and
possibility of using a single tuned mass damper to mitigate the vibrations in
two structural modes having close natural frequencies and mode shapes. The
method is based on the coupled analysis of modal responses under stochastic
loading. Random processes are employed to represent the loading and the
acceleration in the structural mode shapes. After a proper rescaling o ering
an appropriate distinguished limit, a perturbation method of the eigenvalue
problem is developed and the variances of these responses are expressed at
rst order by accurate and simple analytical expressions.