Optimum design of linear tuned mass dampers for structures with nonlinear behaviour

This paper investigates the optimum design of tuned mass dampers (TMDs) for the seismic protection of inelastic structures. A single linear TMD is treated and is assumed to be applied to a single nonlinear degree of freedom system, described by the Bouc–Wen hysteretic model. The seismic load is modelled by a stationary filtered stochastic process to consider its intrinsic stochastic nature. The optimization problem is set by taking into consideration three different possible objective functions (OFs): the maximum of the peak structural displacement standard deviation, the average hysteretic dissipated energy of a protected building with reference to an unprotected one, and a functional damage that considers the two indexes previously described. Different numerical examples and parametric analysis are shown to confront the three optimization criteria and to determine the best tuning frequency and damping ratio of the TMDs to be used in the structure. Results confirm that the application of a TMD system reduces the amount of the hysteretic dissipated energy, which is a direct measure of damage in the structure, and so it is beneficial for the protection of buildings that develop a nonlinear behaviour under severe dynamic loadings.