Soil-structure random response reduction via TMD-VD simultaneous use

A new systematic method for optimal viscous damper (VD) placement in building structures with a tuned mass damper (TMD) is developed taking into account the response amplification due to the surface ground. Non-linear amplification of the surface ground is described by an equivalent linear model and local interaction with the surrounding soil is incorporated with a horizontal spring and a dashpot. Hysteretic damping of the surface ground and radiational damping into the semi-infinite visco-elastic ground are included in the model. An original steepest direction search algorithm is applied to the interaction model with a TMD. Closed-form expressions of the inverse of the coefficient matrix (tri-diagonal matrix) enable one to compute the transfer function and its derivative with respect to design variables very efficiently. It is shown that simultaneous use of a TMD and added viscous dampers is very effective in response reduction and the ratio of the fundamental natural period of the structure to that of the surface ground is a key parameter for characterizing the optimal damper placement. Several examples with and without a TMD for different soil conditions are presented to demonstrate the effectiveness and validity of the present method.