In this paper, a system of magnetically coupled oscillators consisting of a Π-shaped horizontal cantilever and a rectangular vertical cantilever with a frequency ratio of 1:2, is proposed for high-sensitivity mass detection. Through driving the horizontal cantilever directly by a periodic excitation force, two symmetric peaks in its amplitude-frequency curve can be observed due to the energy transfer from it to the vertical beam. The two peaks remain symmetrical with the fluctuation of excitation force but change antisymmetrically after applying mass perturbation on the tip of horizontal beam. Hence, both amplitude difference and frequency sum of those two peaks exhibit differential-like characteristics, and both their differential amplification performance for mass perturbation and their suppression performance for the fluctuation of the excitation force are further compared. The frequency sum-based sensing scheme not only shows better suppression performance, but also can further amplify mass sensitivity through combining frequency multiplication. In addition, effect of modal damping on driving threshold and sensing range is further researched for optimization. Compared to conventional resonant frequency shift-based sensing scheme, the proposed one not only differentially amplifies the mass sensitivity, but also greatly suppresses the effect of driving amplitude fluctuation, indicating great potential for high sensitivity mass detection.

本文提出了一种由频率比为 1:2 的 Π 形水平悬臂和矩形垂直悬臂组成的磁耦合振荡器系统，用于高灵敏度质量检测。通过周期性激振力直接驱动水平悬臂梁，由于能量从悬臂梁到垂直梁的传递，可以观察到其幅频曲线上的两个对称峰值。两个峰值随激振力的波动保持对称，但在水平梁尖端施加质量扰动后发生反对称变化。因此，这两个峰值的幅度差和频率和都表现出类似微分的特性，并进一步比较了它们对质量扰动的差分放大性能和对激振力波动的抑制性能。基于频率和的传感方案不仅表现出更好的抑制性能，而且通过组合倍频可以进一步放大质量灵敏度。此外，进一步研究了模态阻尼对驱动阈值和感应范围的影响以进行优化。与传统的基于谐振频移的传感方案相比，该方案不仅可以差分放大质量灵敏度，而且大大抑制了驱动幅度波动的影响，表明高灵敏度质量检测的巨大潜力。基于频率和的传感方案不仅表现出更好的抑制性能，而且通过组合倍频可以进一步放大质量灵敏度。此外，进一步研究了模态阻尼对驱动阈值和感应范围的影响以进行优化。与传统的基于谐振频移的传感方案相比，该方案不仅可以差分放大质量灵敏度，而且大大抑制了驱动幅度波动的影响，表明高灵敏度质量检测的巨大潜力。基于频率和的传感方案不仅表现出更好的抑制性能，而且通过组合倍频可以进一步放大质量灵敏度。此外，进一步研究了模态阻尼对驱动阈值和感应范围的影响以进行优化。与传统的基于谐振频移的传感方案相比，该方案不仅可以差分放大质量灵敏度，而且大大抑制了驱动幅度波动的影响，表明高灵敏度质量检测的巨大潜力。