A Novel Optimal Design Method for Tuned Mass Dampers With Viscoelastic Motion‐Limiting Stoppers

As one of the most widely implemented passive control systems in structural engineering, Tuned Mass Dampers (TMDs) require precise parameter tuning to maintain optimal performance. However, the incorporation of motion‐limiting stoppers introduces nonlinear effects that alter the system's inherent frequency and damping characteristics, ultimately leading to detuning and compromised control effectiveness. To address this issue, a TMD with piecewise stiffness‐damping (PSDTMD) is proposed to optimize the TMDs with limiting stoppers. Numerical simulation results indicate that the classical linear method fails to design the PSDTMD parameters. Considering the nonlinearity of the PSDTMD, the decoupled motion equation for the PSDTMD is first obtained, and then its frequency response equation is analytically derived using the averaging method. By determining the frequency that maximizes the displacement of the PSDTMD, the analytical optimal frequency ratio is derived from the frequency response equation, and the optimal damping is discussed through comparisons with the classical linear design. Furthermore, the effectiveness of the PSDTMD using the novel design method is investigated using a single‐degree‐of‐freedom (SDOF) structure and a nine‐story benchmark structure. The control performance of the PSDTMD designed by the novel method is compared to that designed by the classical linear method. Results show that the control performance of the PSDTMD designed by the novel method is greatly improved. Besides, results show that the PSDTMD can significantly reduce the tuned mass stroke compared to the conventional TMD. In conclusion, the novel design method can consider the adverse effects of the viscoelastic motion‐limiting stoppers and improve the control performance of TMDs, which is meaningful for the engineering application of TMDs.