Harmonic balance method for MEMS oscillators

Introduction Micro-Electro-Mechanical System (MEMS) oscillators play a pivotal role in diverse applications such as biosensors and wearable sensors. To optimize their performance and ensure reliability, exploring their periodic properties and pull-in instability during the study of MEMS oscillators with singularity is crucial. The harmonic balance method, a prevalent approach for analyzing nonlinear systems, is selected as the research focus. Methods This study conducts an in-depth theoretical analysis of the harmonic balance method applied to MEMS oscillators. The treatment of singular terms and the selection of approximate solutions within this method are meticulously examined. Results The analysis reveals that the handling of singular terms and the choice of approximate solutions in the harmonic balance method have a significant impact on the accuracy of determining the pull-in condition. Incorrect choices can lead to large errors, while a well-chosen approximate solution can remarkably improve the accuracy of predicting pull-in instability. Discussion The research findings provide valuable insights for enhancing the application of the harmonic balance method in the analysis of MEMS oscillators. These results can serve as references for future studies aiming to further optimize the performance and reliability of MEMS oscillator-based devices.