This paper investigates the optimal design of the tuned viscous mass damper (TVMD) with linear and nonlinear viscous damping subjected to white‐noise excitation. The TVMD consists of a parallel‐connected inerter and dashpot, and a spring attached to the main structure. To examine the vibration control performance of the TVMD, both theoretical analysis and numerical optimization are conducted to obtain the optimal parameters. In this paper, a closed‐form solution of optimal design for the linear TVMD is proposed. Compared with the traditional TMD, the optimized linear TVMD has comparable and even better control performance, but less damping and real physical mass are required. For the nonlinear TVMD, the influences of the damping exponent on the optimal parameters and control performance are analyzed. The results show that the optimal damping coefficient is significantly affected by the damping exponent and associated with the inherent structure damping ratio and the given mass ratio. However, the damping exponent has few effects on the optimal frequency ratio and the control performance. To well understand the control principle of the nonlinear TVMD, a numerical example under harmonic excitations is considered, and the results show that the damping exponent is related to negative stiffness, which dominates the control performance of TVMD. Under several natural ground motions selected, the analytical results show that the nonlinear TVMD does not always improve the control performance compared with the linear TVMD, particularly for a stronger earthquake than the designed for. Nevertheless, in such case, larger values of damping exponent, 2.0 for instance, can significantly suppress the internal force transferred to the main structure with a smaller sacrifice of control effectiveness. The main structure and the TVMD device can then be simultaneously protected to some degree.

中文翻译：

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具有白噪声激励的具有线性和非线性粘滞阻尼的TVMD的优化设计

本文研究了具有线性和非线性粘性阻尼的白噪声激励下的调谐粘性质量阻尼器（TVMD）的优化设计。TVMD由并联的惰轮和减震器以及连接到主体结构的弹簧组成。为了检查TVMD的振动控制性能，进行了理论分析和数值优化，以获得最佳参数。本文提出了线性TVMD优化设计的闭式解。与传统的TMD相比，优化的线性TVMD具有相当甚至更好的控制性能，但所需的阻尼和实际质量却更少。对于非线性TVMD，分析了阻尼指数对最优参数和控制性能的影响。结果表明，最佳阻尼系数受阻尼指数的显着影响，并与固有结构阻尼比和给定质量比有关。但是，阻尼指数对最佳频率比和控制性能几乎没有影响。为了更好地理解非线性TVMD的控制原理，以谐波激励下的数值算例为例，结果表明阻尼指数与负刚度有关，支配着TVMD的控制性能。在选定的几种自然地面运动下，分析结果表明，与线性TVMD相比，非线性TVMD并不总是能够改善控制性能，尤其是在地震强度大于设计值的情况下。但是，在这种情况下，阻尼指数的值较大，为2。例如，0可以显着抑制传递到主结构的内力，而牺牲的控制效果较小。然后可以在某种程度上同时保护主体结构和TVMD装置。