Passive damping systems are energy dissipating devices that are used in building constructions to reduce excessive vibration caused by wind or earthquakes.Recently, the use of inerters, devices using the inertia of the rotating mass, as a passive damping system has become more and more popular. Inerter, regardless of the construction, generates a resistance force that is proportional to the relative acceleration at the terminal ends of the device.The purpose of this study is to evaluate the effectiveness of the viscoelastic (VE) dampers in combination with the inerter. For the derived equations of motion of structures with VE dampers and inerters, the Laplace transformation is applied, which leads to a nonlinear eigenproblem. The solution to the eigenproblem is obtained using the continuation method, also known as the homotopy or as the path following method.It was found that for some cases of inerter connection with ve damper, there are some additional solutions in relation to the degrees of freedom of the structure. Furthermore, the dynamic characteristics of the structure associated with the above-mentioned additional eigenvalue are strongly dependent on the equivalent inerter mass.Damping efficiency is tested by determining changes in the system’s dynamic characteristics: natural frequencies, non-dimensional damping ratios and displacement transfer functions. The presented approach allows determining the appropriate parameters of the inerter and VE damper and their appropriate location on the structures that correspond to the most effective damping. The obtained numerical results confirm the effectiveness of the proposed approach.

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结合粘弹性阻尼器和惰性器的被动阻尼系统的有效性

被动阻尼系统是一种能量消散装置，用于建筑结构中，以减少风或地震引起的过度振动。最近，使用惯性装置，利用旋转质量的惯性的装置，作为被动阻尼系统变得越来越流行. 无论结构如何，惰性器都会产生与装置末端的相对加速度成正比的阻力。本研究的目的是评估粘弹性 (VE) 阻尼器与惰性器组合的有效性。对于具有 VE 阻尼器和惯性器的结构的推导运动方程，应用了拉普拉斯变换，这导致了非线性特征问题。使用延拓法得到特征问题的解，也称为同伦法或路径跟随法。研究发现，对于某些与 ve 阻尼器的惯性连接的情况，对于结构的自由度，还有一些额外的解决方案。此外，与上述附加特征值相关的结构的动态特性强烈依赖于等效惯性质量。通过确定系统动态特性的变化来测试阻尼效率：固有频率、无量纲阻尼比和位移传递函数. 所提出的方法允许确定惰性和 VE 阻尼器的适当参数以及它们在与最有效阻尼相对应的结构上的适当位置。获得的数值结果证实了所提出方法的有效性。