Exact and Approximate Analysis of Structural Models with Linear Viscous or Viscoelastic Dampers and Singular Mass Matrices

This research is concerned with model reduction methods in analysis of structural models with viscous or viscoelastic damping and singular mass matrices. These types of models are commonly used in the preliminary design of building structures containing supplemental damping devices to define locations and parameters of the energy dissipaters. In this paper we develop an exact reduced-order technique for the modal analysis of models with singular mass matrices and viscous or viscoelastic supplemental dampers. Using static condensation of generalized coordinates without mass and no damper connection, and using a transformation using the eigenvectors of the damping matrix, an exact state-space formulation with non-singular mass matrix is developed. The above-mentioned alternative model-reduction strategies are revisited and the accuracy of these methods in the estimation of poles (natural frequencies and damping ratios) and frequency response functions is compared with the exact model. To compare the accuracy of the alternative models developed a simple benchmark structural model with singular mass matrix is used.