Dampers with negative stiffness behavior have been widely investigated for structural vibration control due to their superior performance. In practical applications, a support in series with these dampers might have some flexibility, that is, the stiffness is positive but finite. This paper investigates the effects of that flexibility on the performance of a passive negative stiffness damper (PNSD). First, a system consisting of a PNSD in series with a flexible support is presented, and the lower limit of the support stiffness needed to keep the system stable is derived. Second, a mechanical model for the proposed system is analyzed theoretically. An equivalent model of the damping force is established. The deformation of the flexible link is illustrated, followed by a demonstration of its effect on the hysteresis loops. Finally, an experimental investigation is performed to evaluate the performance of the PNSD support system. A device that contains an oil damper and two compressed springs is utilized to provide negative stiffness and Coulomb friction behavior. One of the set of springs is then incorporated to act as a positive but finite stiffness support in series with the device. Tests are conducted to assess the hysteretic behavior of the overall system. Theoretical and experimental results indicate that a range of equivalent negative stiffness and Coulomb friction level can be achieved simply, depending upon the positive stiffness of the flexible support in series with the PNSD.

中文翻译：

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被动负刚度阻尼器与柔性支撑件串联：理论和实验研究

具有负刚度特性的阻尼器由于其卓越的性能已被广泛研究用于结构振动控制。在实际应用中，与这些阻尼器串联的支座可能具有一定的柔韧性，即刚度为正但有限。本文研究了这种灵活性对被动负刚度阻尼器（PNSD）性能的影响。首先，提出了一种由PNSD与柔性支撑串联而成的系统，并得出了保持系统稳定所需的支撑刚度下限。其次，从理论上分析了所提出系统的机械模型。建立了等效的阻尼力模型。图示了柔性连杆的变形，然后演示了其对磁滞回线的影响。最后，进行实验研究以评估PNSD支持系统的性能。包含油阻尼器和两个压缩弹簧的设备可用于提供负刚度和库仑摩擦性能。然后并入一组弹簧中的一个，以充当与装置串联的正但有限的刚度支撑。进行测试以评估整个系统的磁滞行为。理论和实验结果表明，取决于与PNSD串联的柔性支座的正刚度，可以简单地实现一系列等效的负刚度和库仑摩擦水平。包含油阻尼器和两个压缩弹簧的设备可用于提供负刚度和库仑摩擦性能。然后并入一组弹簧中的一个，以充当与装置串联的正的但有限的刚度支撑。进行测试以评估整个系统的磁滞行为。理论和实验结果表明，取决于与PNSD串联的柔性支座的正刚度，可以简单地实现一系列等效的负刚度和库仑摩擦水平。利用一个包含减震器和两个压缩弹簧的装置来提供负刚度和库仑摩擦性能。然后并入一组弹簧中的一个，以充当与装置串联的正的但有限的刚度支撑。进行测试以评估整个系统的磁滞行为。理论和实验结果表明，取决于与PNSD串联的柔性支座的正刚度，可以简单地实现一系列等效的负刚度和库仑摩擦水平。