Analytical modeling of mechanical behavior for MEMS/NEMS-based single-clamped multilayer resonators with symmetrical complex shapes

Several micro/nano-electromechanical systems (MEMS/NEMS) devices are composed by complex-shaped multilayer resonators such as energy harvesters, gas and biological sensors, magnetic field sensors, accelerometers, and viscosity sensors. These devices require analytical models to predict the best mechanical performance, improving their sensitivity and resolution. Here, we present the analytical modeling to determine the mechanical behavior of MEMS/NEMS-based single-clamped multilayer resonators with symmetrical complex shapes. This modeling can estimate the first bending resonant frequency and out-plane deflections of multilayer resonators using the Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory. In addition, the quality factors of these multilayer resonators are calculated considering the air damping at atmospheric pressure. Also, finite element method (FEM) models are developed to obtain the mechanical behavior of the resonators. The results of our analytical models agree well with those of FEM models and experimental data reported in the literature. The proposed analytical modeling can be used to enhance the mechanical response of MEMS/NEMS devices formed by multilayer resonators with symmetrical complex cross-sections.