A mass multi-warning scheme based on one-to-three internal resonance

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.