A novel design procedure for tuned mass dampers in isolated structures is presented. The proposed optimization method is specifically developed to control base displacements or to solve the large isolator displacement problem in this type of structures under earthquakes. Therefore, it is based on a displacement transmissibility function, T, a particular case of the general transmissibility concept, which comes from Vibration Isolation. Three contributions are application of new seismic displacement narrowbandness, simpler relative transmissibility function, and compound design of isolation plus tuned mass damper. A standard isolated model is used to show that the base displacement can be controlled at levels in the proximity of the ground motion ( T ≈ 1), which results in a positive comparison with previous isolation and tuned mass damper solutions; this is one of the main conclusions and it is based on novelty three above; in fact, other solutions in the literature compare their attained displacements with respect to the structure without tuned mass damper. Comparison with isolated results is not, therefore, possible herein, but it is not desirable either; actually, what is possible is a positive and more demanding comparison, which is with respect to the very seismic ground displacement itself. The large isolator displacement problem can be solved or attenuated by properly designing a tuned mass damper subsystem jointly with the isolation one.
The first with displacement problem for a third-order parabolic-hyperbolic equation and the effect of inequality of characteristics as data carriers of the Tricomi problem
