Abstract

The traditional nonlinear energy sink (NES), i.e., a smooth and cubic NES, can cause stable higher branch of response of primary systems with increasing excitation forcing. For this reason, the traditional NES is only effective in a certain excitation range. A kind of non-smooth NES with descending stiffness is proposed for expanding this effective range. The non-smooth NES has a higher cubic nonlinear stiffness in the initial range, and the stiffness is reduced as its amplitude exceeds the initial range. The governing equation of motion for a linear primary oscillator attached to the non-smooth NES is obtained in the case of harmonic excitation. The complexification-averaging method is used to obtain the steady-state equation of the system. A least square-based program with the help of a Runge–Kutta-based program is used to analyze the dynamic behaviors of the system. The results demonstrate that the non-smooth NES can eliminate the stable higher branch, therefore expanding the effective excitation range, until the excitation amplitude increases to a very high level. The influences of the piecewise boundary and the stiffness of the secondary stage of the non-smooth NES on the vibration absorption performance are investigated, and the drawbacks of this NES design are discussed. Finally, a structural design based on the theoretical results of the non-smooth NES is proposed, which is composed of permanent magnets, a smooth and discontinuous oscillator and linear springs.

中文翻译：

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刚度递减的非光滑非线性能量池的性能

摘要

传统的非线性能量吸收器（NES），即平滑的立方NES，可以随着激励强迫的增加而引起初级系统响应的稳定较高分支。因此，传统的NES仅在一定的激发范围内有效。为了扩展该有效范围，提出了一种刚性下降的非光滑NES。非光滑NES在初始范围内具有较高的立方非线性刚度，并且当其振幅超过初始范围时，刚度会降低。在谐波激励的情况下，获得了连接到非平滑NES的线性主振荡器的运动控制方程。复数平均法用于获得系统的稳态方程。在基于Runge–Kutta的程序的帮助下，基于最小二乘的程序用于分析系统的动态行为。结果表明，非光滑的NES可以消除稳定的较高分支，从而扩大有效激发范围，直到激发幅度增加到很高的水平为止。研究了非光滑NES的分段边界和次级刚度对减振性能的影响，并讨论了这种NES设计的弊端。最后，基于非光滑NES的理论结果，提出了一种结构设计，该结构由永磁体，光滑且不连续的振荡器和线性弹簧组成。因此，扩大有效激励范围，直到激励幅度增加到很高的水平。研究了非光滑NES的分段边界和次级刚度对减振性能的影响，并讨论了这种NES设计的弊端。最后，基于非光滑NES的理论结果，提出了一种结构设计，该结构由永磁体，光滑且不连续的振荡器和线性弹簧组成。因此，扩大有效激励范围，直到激励幅度增加到很高的水平。研究了非光滑NES的分段边界和次级刚度对减振性能的影响，并讨论了这种NES设计的弊端。最后，基于非光滑NES的理论结果，提出了一种结构设计，该结构由永磁体，光滑且不连续的振荡器和线性弹簧组成。