Acceleration sensing based on the bifurcation dynamics of parametrically excited mode-localized resonators

Abstract

A parametrically excited mode-localized accelerometer is designed using the bifurcation phenomenon to improve the robustness of the fluctuation of the driving voltage and damping while maintaining high sensitivity. A dynamic multi-physics model was established while considering both mechanical and electrostatic nonlinearities. The equation was solved by method of multiple scales and verified by harmonic balanced method coupled with the asymptotic numerical method. Two types of bifurcation exist in amplitude frequency response, namely Saddle-Node bifurcation and Supercritical Hopf bifurcation. By introducing Saddle-Node bifurcation, the response amplitude and measurement range can be improved by 100% and 1000%, respectively, while the sensitivity of the amplitude ratio is about 2 orders of magnitude higher than that based on the frequency ratio. At the Supercritical Hopf bifurcation point, a small acceleration will change the topological structure from Supercritical Hopf to Saddle-Node bifurcation. The variation in the amplitude ratio of the Supercritical Hopf point with acceleration is similar to the sign function, which leads to an extremely high sensitivity of 10000%/g in a dynamic range of ±0.001 g. Moreover, the Supercritical Hopf bifurcation point is not affected by the amplitude of the excitation voltage and damping coefficient, which provides a new method for improving the sensing robustness. Ethical Compliance: All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. Conflict of Interest declaration: The authors declare that they have NO affiliations with or involvement in any organization or entity with any financial interest in the subject matter or materials discussed in this manuscript.