Nonparametric identification of a MEMS resonator actuated by levitation forces

This work presents nonparametric identification of a Micro-Electro-Mechanical Systems (MEMS) beam subjected to a non-classical nonlinear electrostatic (levitation) force. The approach is based on the Restoring Force Surface method and the Chebyshev polynomials. The study examines the main challenges associated with the used approach as applied to small-scale systems, such as the inability to measure the restoring force and acceleration. In this work, we use a mix of analytical techniques, experimental data, and Lagrange polynomial interpolation to estimate the restoring forces of the system and its nonlinearities. The extracted results are compared with the measurements, which show excellent agreement. Results are shown for several cases of forcing strength (voltage loads). The results reveal for some cases quadratic terms for the velocity indicating nonlinear damping, which cannot be revealed using parametric identification methods with a priori assumed forms. It is shown that the extracted nonlinear model is robust enough to predict the dynamical behavior of the beam even when the voltage load is increased to nearly 300 % more than the one used for model identification. The presented approach can be applied to other micro and nano systems to identify their characteristics and reveal their nonlinear stiffness and damping parameters.