An analytical model for the resonance frequency of square perforated Lamé-mode resonators

•We create an analytical model for a perforated structure as an equivalent material.•We use this model to determine the resonance frequencies of perforated Lamé mode resonators.•The model allows fast design of MEMS resonators for frequency reference and mass sensing. In this work, simple analytical models based on the concept of an equivalent material are used to describe the mechanical behavior of resonators perforated by a regular array of square holes, a common occurrence in several MEMS devices and sensors. This description is applied to the determination of the resonance frequency of Lamé-mode square resonators, which are frequently pursued as high-Q MEMS resonators. The models predictions are compared with FEM simulations and experimental data both from the literature and from measurements obtained by the authors on thick SOI MEMS resonators. The models predictions are in good accordance both with FEM results and with experimental data.