A linear model for multiple degree-of-freedom weakly coupled resonators based accelerometers

Multiple degree-of-freedom (multi-DoF) weakly coupled resonators (WCRs) system based on mode-localization has been widely used in resonant sensing and is increasingly promising to be implemented as an ultrasensitive accelerometer. Previously, 2-, 3- and 4-DoF WCRs accelerometers have been proposed, exhibiting excellent sensitivity. However, the analytical model for multi-DoF WCRs, e.g., 5-DoF, as well as its linearized closed-form solution of resonant frequency and amplitude ratio are still lacking, which hinders the parametric optimization of this type of accelerometer. In this paper, we proposed a linearized mathematical model for a typical WCRs system with arbitrary DoF. This is mainly derived based on approximation according to the special mathematical characteristics of WCRs. Based on the combination of analytical and numerical calculations, the effects of different stiffness parameters are revealed. The linearized model is further verified by those reported WCRs with lower DoF elsewhere.