A tuned mass damper is a passive control device that has been widely used in aerospace, mechanical, and civil engineering as well as many other fields. Tuned mass dampers have been studied and improved over the course of many years. In practical engineering applications, a tuned mass damper inevitably produces some nonlinear characteristics due to the large displacement and the use of the limiting devices, but this nonlinearity is often neglected. The simulation results in this study confirm that neglecting the nonlinearity in the design process can produce adverse effects on the control performance. This paper takes into account the nonlinearity of the tuned mass damper produced in the process of vibration and deduces an optimum formula for the frequency of a tuned mass damper by the complexification averaging method and multiscale method. Based on this formula, a modified design method for the frequency of a tuned mass damper is presented. The numerical results show that the nonlinear tuned mass damper after modification is better than a linear tuned mass damper in terms of control performance.

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非线性调谐质量阻尼器设计的解析分析

调谐质量阻尼器是一种被动控制设备，已广泛用于航空航天，机械和土木工程以及许多其他领域。经过多年的研究，已对调谐质量阻尼器进行了研究和改进。在实际工程应用中，由于大位移和限制装置的使用，调谐质量阻尼器不可避免地会产生一些非线性特性，但是这种非线性通常被忽略。本研究中的仿真结果证实，在设计过程中忽略非线性可能会对控制性能产生不利影响。本文考虑了振动过程中产生的调谐质量阻尼器的非线性，并通过复数平均法和多尺度方法推导了调谐质量阻尼器频率的最佳公式。基于该公式，提出了一种调谐质量阻尼器频率的改进设计方法。数值结果表明，改进后的非线性调谐质量阻尼器在控制性能方面优于线性调谐质量阻尼器。