On performance comparison of tuned mass dampers (TMD) enhanced with inerter and negative stiffness device

Abstract

Tuned mass dampers (TMDs) are widely used vibration control devices in engineering applications. However, traditional TMDs have inherent limitations, such as requiring a large mass to achieve high control performance, narrow frequency bandwidth, and poor robustness. Inerters and negative stiffness devices (NSDs) have recently been introduced to upgrade traditional TMDs, resulting in the development of tuned mass dampers enhanced with inerter (TMDI) and tuned mass dampers enhanced with negative stiffness (TMDNS). Existing studies have shown that both inerters and NSDs can effectively reduce the large mass requirement and improve the robustness of traditional TMDs. However, a fair comparative analysis of the control effectiveness between TMDI and TMDNS within a unified framework remains lacking. To address this research gap, this study proposes a unified optimization design method and conducts comparative studies on the control effectiveness of TMDI and TMDNS. Specifically, the analytical models of a single-degree-of-freedom (SDOF) system incorporating either TMDI or TMDNS are first established, and corresponding equations of motion are derived. A unified optimization design method, namely the Equal-Peak Dynamic Amplification Factor (Equal-PDAF) method, is then proposed to determine the optimal design parameters, including the optimal inertance ratio and negative stiffness ratio. The control performance, robustness, and enhancement mechanisms of TMDI and TMDNS under steady-state excitations are systematically evaluated. Finally, the seismic performances of TMDI and TMDNS under natural seismic records are compared. The results show that both TMDI and TMDNS significantly reduce the large mass requirement for achieving high control performance by increasing the control force and approaching the optimum phase difference. Moreover, TMDI demonstrates superior performance in improving control effectiveness and reducing auxiliary mass stroke, while TMDNS exhibits better robustness against detuning effects. Furthermore, the optimized TMDI performs slightly better than TMDNS under natural seismic records. In conclusion, both TMDI and TMDNS are promising alternatives to traditional TMDs, offering excellent control performance and robustness in vibration control applications.