Abstract A new mass multi-warning scheme via integrating duffing nonlinearity with 1:3 internal resonance is proposed in this paper, which can achieve the sensing, the first time warning and the second time warning with the increment of mass perturbation. A nonlinear low frequency mode and another linear high frequency mode with a frequency ratio of 1:3 are coupled via cubic nonlinearities. A theoretical expression is established and derived by multi-scale method to predict the amplitude-frequency curve with respect to the effect of mass perturbation. On one hand, both the range of the first time warning and the threshold of the second time warning can be adjusted for different applications through changing the eigen-state frequency value of the high frequency mode. On the other hand, the linearity of mass sensing can be greatly improved by reversing the sign of the coupling term of the high frequency mode to the low frequency mode. A П-shaped coupled beam structure, consisting of a П-shaped beam and a rectangular beam that coupled by two overhangs, is further proposed for preliminarily physical realization. Compared to conventional bifurcation-based single warning scheme, the multi-warning scheme proposed in this paper is more capable of satisfying complex warning and sensing requirements in various applications, such as both the detection and the multi-warning of gas leak, dust pollution, harmful chemicals and so on.

中文翻译：

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一种基于一比三内共振的大规模多重预警方案

摘要 本文提出了一种将duffing非线性与1:3内共振相结合的质量多重预警方案，实现了质量扰动增量的感知、第一次预警和第二次预警。一个非线性低频模式和另一个频率比为 1:3 的线性高频模式通过三次非线性耦合。通过多尺度方法建立并推导出理论表达式，以预测质量扰动影响的幅频曲线。一方面，通过改变高频模式的本征态频率值，可以针对不同的应用调整第一次警告的范围和第二次警告的阈值。另一方面，通过将高频模式耦合项的符号反转为低频模式，可以大大提高质量传感的线性度。进一步提出了一种由 П 型梁和由两个悬垂耦合的矩形梁组成的 П 型耦合梁结构，用于初步物理实现。与传统的基于分叉的单一预警方案相比，本文提出的多预警方案更能满足各种应用中复杂的预警和感知需求，如气体泄漏、粉尘污染、粉尘污染等的检测和多预警。有害化学物质等。进一步建议用于初步物理实现。与传统的基于分叉的单一预警方案相比，本文提出的多预警方案更能满足各种应用中复杂的预警和感知需求，如气体泄漏、粉尘污染、粉尘污染等的检测和多预警。有害化学物质等。进一步建议用于初步物理实现。与传统的基于分叉的单一预警方案相比，本文提出的多预警方案更能满足各种应用中复杂的预警和感知需求，如气体泄漏、粉尘污染、粉尘污染等的检测和多预警。有害化学物质等。