Optimal Design Formula for Tuned Mass Damper Based on an Analytical Solution of Interaction between Soil and Structure with Rigid Foundation Subjected to Plane SH-Waves

The tuned mass damper (TMD) is widely used for vibration mitigation, especially in high-rise buildings where significant soil-structure interaction (SSI) effects are usually involved. This creates a need to consider SSI effects in TMD design. In this work, a novel design framework for TMD systems with SSI effects is proposed. For response evaluations, structure-TMD systems are modeled as a two-degrees-of-freedom (2DOF) system, standing on a rigid foundation and subject to out-of-plane SH seismic wave inputs in a homogeneous half-space. Closed-form analytical solutions of its displacement and acceleration responses are derived, and the H2-norm of the system transfer function is introduced to quantify the performances of TMDs. The TMD design problem is then formulated and solved by optimizing the performances. Considering that aspects other than response mitigation, e.g., strokes, damper device costs, etc., may be critical to TMD damping ratios, a design framework is developed by firstly making an informed selection on TMD damping ratios, and subsequently tuning TMD frequency ratios through calibrated formulae. In addition, TMD strokes versus TMD damping ratios are investigated to facilitate the determination of TMD damping ratios. A case study based on a real-existing building system is carried out to illustrate the application of the proposed design framework. The framework has proven to be highly efficient and effective and suitable to for use in practical engineering.