The mechanical behavior analysis of the partially center electrode-covered CMUTs based on Ritz method

As a quintessential electrostatic excitation micro electro mechanical system device, the capacitive micromachined ultrasonic transducers (CMUTs) is extensively utilized across medical, industrial, military and numerous other fields. To comprehensively analyze the fundamental properties of CMUTs, it is imperative to investigate their precise mechanical behavior under electrostatic forces. When the fringing field effect of the CMUT is ignored, this manuscript introduces the electromechanical coupling model of the partially center electrode-covered CMUTs (PCEC-CMUTs) to analyze its fundamental properties under nonlinear electrostatic forces for the first time. Utilizing the Ritz method, a novel segmentation function is employed to express the electrostatic deflections of the PCEC-CMUTs. Through the solution results of this model, fundamental performance parameters such as collapse voltage, electrostatic deflection and resonant frequency can be rapidly obtained. Subsequently, the finite element model (FEM) with COMSOL 6.1a is used to validate the theoretical model. The relative errors of electrostatic deflections and resonant frequency between the theoretical model and the FEM are controlled less than 5% in the region less than 95% of the collapse voltage, which proves the correctness of the theoretical model. These theoretical analyses are instrumental for the design and optimization of electrostatically actuated micro-devices such as CMUTs, and provide a theoretical foundation for establishing immersion equivalent circuits for PCEC-CMUT cells and arrays.