Abstract This study proposes an improved equivalent simplified method coupled with the finite element method (ESM-FEM) to investigate the control performance of the particle tuned mass damper (PTMD) attached to the multi-degree-of-freedom (MDOF) structure (e.g. transmission tower). To validate the proposed method, the coupled system responses from the ESM-FEM method are compared to the results of the previous study under the free vibration and seismic excitation. The transmission tower is modeled by the FEM in Abaqus, while the PTMD is simulated by the ESM in Python. The damping mechanism of the PTMD-MDOF system is investigated based on the ESM-FEM method, and the PTMD’s control effect is evaluated. Besides, the reliability of the system’s control performance is also discussed. The results show that the ESM-FEM method is reasonable for evaluating the damping performance of the coupled system, and its accuracy is validated by the experimental data and Matlab program. Meanwhile, the proposed method makes it easier to obtain the damping force to further better understand the damping mechanism of the coupled system. Furthermore, the PTMD system has good robustness, and its control performance is less sensitive to unpredictable seismic excitations.

中文翻译：

---

MDOF系统中粒子调谐质量阻尼器地震控制的改进ESM-FEM方法

摘要 本研究提出了一种改进的等效简化方法，结合有限元法 (ESM-FEM) 来研究附着在多自由度 (MDOF) 结构上的粒子调谐质量阻尼器 (PTMD) 的控制性能（例如铁塔）。为了验证所提出的方法，将 ESM-FEM 方法的耦合系统响应与先前在自由振动和地震激发下的研究结果进行比较。输电塔由 Abaqus 中的 FEM 建模，而 PTMD 由 Python 中的 ESM 模拟。基于ESM-FEM方法研究了PTMD-MDOF系统的阻尼机理，评价了PTMD的控制效果。此外，还讨论了系统控制性能的可靠性。结果表明，ESM-FEM方法用于评估耦合系统的阻尼性能是合理的，其准确性得到了实验数据和Matlab程序的验证。同时，所提出的方法更容易获得阻尼力，以进一步更好地理解耦合系统的阻尼机制。此外，PTMD系统具有良好的鲁棒性，其控制性能对不可预测的地震激励不太敏感。