On non-linear dynamics of coupled 1+1DOF versus 1+1/2DOF Electro-Mechanical System

The electro-mechanical systems (EMS) are used from nano-/micro-scale (NEMS/MEMS) up to macro-scale applications. From mathematical view point, they are modelled with the second order differential equation (or a set of equations) for mechanical system, which is nonlinearly coupled with the second or the first order differential equation (or a set of equations) for electrical system, depending on properties of the electrical circuit. For the sake of brevity, we assume a 1DOF mechanical system, coupled to 1 or 1/2DOF electrical system (depending whether the capacitance is, or is not considered). In the paper, authors perform a parametric study to identify operation regimes, where the capacitance term contributes to the non-linear behaviour of the coupled system. To accomplish this task, the classical method of multiple scales is used. The parametric study allows us to assess for which applications the capacitance term needs to be considered and in contrary, when the investigation of the coupled system can be simplified neglecting the capacitance of the electrical system and treating the electric circuit as a diffusion type system (i.e. contributing with 1/2DOF). The outcomes presented in this study can be generalized also for multi DOF systems.