A novel optimal design method for tuned mass dampers with elastic motion-limiting stoppers

Tuned Mass Dampers (TMDs) are commonly used passive control devices in practical engineering applications. However, motion-limiting stoppers are usually installed to control the excessive TMD displacement due to the building space limitation, resulting in piecewise nonlinearity and detuning of TMD. This paper studies the influence of elastic motion-limiting stoppers on the optimal design of TMDs through a piecewise stiffness TMD (PSTMD) model. Performance of a PSTMD with classical design is first investigated and proven to be ineffective. To optimize the PSTMD parameters, the motion of PSTMD is decoupled from the controlled structure, and the frequency response equation of PSTMD is obtained analytically through the averaging method. Subsequently, the solution of the optimal design frequency for PSTMD is transformed into the solution of the jump frequency in the frequency response equation. With the optimal frequency of PSTMDs, the optimal damping and control performance of PSTMDs are discussed and analyzed compared with classical linear design, which fully showcases the effectiveness of the novel design method. Finally, the effectiveness of the novel design method is verified using a nine-story benchmark frame structure, and the results demonstrate that the control performance of the optimal PSTMD can be improved by nearly $10\%$ under specific seismic excitation, compared to the PSTMD with classical linear method. In summary, the novel design method can effectively take into account the influence of piecewise nonlinearity caused by elastic motion-limiting stoppers and improve the optimal control performance of TMD in a more realistic engineering environment.