In this paper, a symmetrical twin-tower structure with chassis connected with passive dampers is coupled as 2-DOF (degree of freedom) model. Using the stationary white noise as seismic excitation, the frequency–response function and the vibration energy expression of the symmetrical twin-tower structure are established based on the simplified 2-DOF model. Furthermore, based on the principle of minimum energy, the analytical expressions of the optimization parameters of two kinds of passive dampers are deduced, and the effectiveness of the dampers with optimized coefficients on structural control is verified by numerical examples of 2-DOF and MDOF (multi-degree-of-freedom) systems, respectively. Finally, the control effects of the two kinds of dampers under different control strategies on the responses of displacement of the top, base shear, structural vibration energy, and maximum inter-story drift of the symmetrical twin-tower structure are discussed through three-dimensional finite element numerical examples. It is verified that the analytical expressions of optimum parameters of the two kinds of dampers proposed based on the 2-DOF model are also beneficial to reduce the responses of the MDOF systems and actual engineering.

中文翻译：

---

底盘双塔结构被动控制分析与设计

在本文中，一个对称的双塔结构，底盘连接被动阻尼器，耦合为2-DOF（自由度）模型。以平稳的白噪声为地震激励，基于简化的2-DOF模型建立了对称双塔结构的频率响应函数和振动能量表达式。此外，基于能量最小原理，推导了两种被动阻尼器优化参数的解析表达式，并通过2-DOF和MDOF的数值算例验证了优化系数阻尼器对结构控制的有效性（多自由度）系统，分别。最后，两种阻尼器在不同控制策略下对顶、底剪力位移响应的控制效果，通过三维有限元数值算例，讨论了对称双塔结构的结构振动能量和最大层间漂移。验证了基于2-DOF模型提出的两种阻尼器的最优参数解析表达式也有利于降低多自由度系统的响应和实际工程。