Purpose

The negative stiffness integrated tuned mass damper (NS-TMD) is considered as an interesting and efficient device for passive vibration control. However, design/optimization of NS-TMD may not always lead towards robust performance if there exist uncertainties. In this study, a stochastic design of NS-TMD is proposed taking into account various types of uncertainties.

Methods

Taylor-expansion is used to perturb the objective function facilitating a stochastic design/optimization. Besides, an interval-extension is used to observe the effect of uncertainties with different intensities. The Lyapunov equation is used in the proposed design of NS-TMD by minimizing the dispersion of displacement of primary system. The present work takes into account a standard model of NS-TMD in view of wider applicability of the present study. Random vibration is considered in both the cases of: (a) base-excitation and (b) superstructure loading.

Results

A numerical investigation is further carried out to observe the consequences of uncertainties on optimum design of NS-TMD parameters for both the cases of base-excitation and superstructure loading. Efficiency of NS-TMD is compared under various levels of uncertainties. Besides, some significant earthquake records and white noise (WN) samples are utilized towards more realistic understanding on the performance of stochastic design of NS-TMD under seismic excitation with different level of uncertainties. NS-TMD appears to be effective in robustness against uncertainties in structural parameters in comparison with the frequently used TMD system.

Conclusion

The proposed methodology may be considered as a useful alternative for stochastic design of the NS-TMD under both superstructure loading and base-excitation.

中文翻译：

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负刚度集成调谐质量阻尼器（NS-TMD）的随机设计

目的

负刚度集成调谐质量阻尼器 (NS-TMD) 被认为是一种有趣且有效的被动振动控制装置。然而，如果存在不确定性，NS-TMD 的设计/优化可能并不总是导致稳健的性能。在这项研究中，考虑到各种类型的不确定性，提出了 NS-TMD 的随机设计。

方法

泰勒展开用于扰动促进随机设计/优化的目标函数。此外，使用区间扩展来观察不同强度的不确定性的影响。Lyapunov 方程用于 NS-TMD 的建议设计，通过最小化主系统位移的分散。鉴于本研究的更广泛适用性，目前的工作考虑了 NS-TMD 的标准模型。在以下两种情况下都考虑了随机振动：(a) 基础激励和 (b) 上部结构加载。

结果

进一步进行数值研究以观察不确定性对基础激励和上部结构加载情况下 NS-TMD 参数优化设计的影响。在各种不确定性水平下比较 NS-TMD 的效率。此外，一些重要的地震记录和白噪声 (WN) 样本被用于更真实地了解 NS-TMD 随机设计在具有不同不确定性水平的地震激发下的性能。与常用的 TMD 系统相比，NS-TMD 似乎在对抗结构参数不确定性的鲁棒性方面是有效的。

结论

所提出的方法可以被认为是在上部结构加载和基础激励下随机设计 NS-TMD 的有用替代方案。