Purpose

Inerter-based dynamic vibration absorber (IDVA) has been widely used to reduce the responses of vibration systems. Its application to the nonlinear system is underexamined and will be explored.

Methods

In the present investigation, an IDVA is applied to a randomly excited nonlinear system which is of concern. The random response of the nonlinear system is analyzed by introducing a generalized harmonic transformation and establishing the relationships between the responses of the nonlinear main system and the IDVA secondary system.

Results

Numerical results are given to illustrate the applicability and effectiveness of the proposed method. The influences of the parameters of the IDVA, the main nonlinear system, and the excitation on the mean-square displacement response of the nonlinear system are investigated. Furthermore, the suppression effectiveness of the IDVA is discussed in detail.

Conclusion

Comparison of the approximate analytical results and simulation results shows that the proposed method is accurate and effective in quite large parameter ranges. Moreover, it is found that the response suppression effectiveness of the IDVA is robust to the main system nonlinearity and to the intensity of the random excitation.

中文翻译：

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基于惯性的动态减振器非线性系统的随机响应

目的

基于惯性的动态吸振器（IDVA）已被广泛用于减少振动系统的响应。它在非线性系统中的应用尚未得到充分研究，将予以探索。

方法

在本研究中，IDVA 应用于随机激发的非线性系统。通过引入广义谐波变换，建立非线性主系统响应与IDVA二次系统响应关系，分析非线性系统的随机响应。

结果

给出了数值结果来说明所提出方法的适用性和有效性。研究了IDVA参数、主非线性系统和激励对非线性系统均方位移响应的影响。此外，详细讨论了 IDVA 的抑制效果。

结论

近似解析结果和仿真结果的比较表明，该方法在相当大的参数范围内是准确有效的。此外，还发现 IDVA 的响应抑制有效性对主系统非线性和随机激励强度具有鲁棒性。