Closed-Form Expressions on CMUTs With Layered Anisotropic Microplates Under Residual Stress and Pressure

Capacitive micromachined ultrasonic transducers (CMUTs) are promising in the emerging fields of personalized ultrasonic diagnostics, therapy, and noninvasive 3-D biometric. However, previous theories describing their mechanical behavior rarely consider multilayer and anisotropic material properties, resulting in limited application and significant analysis errors. This article proposes closed-form expressions for the static deflection, collapse voltage, and resonant frequency of circular-microplate-based CMUTs, which consider both the aforementioned properties as well as the effects of residual stress and hydrostatic pressure. These expressions are established by combining the classical laminated thin plate (CLTP) theory, Galerkin method, a partial expansion approach for electrostatic force, and an energy equivalent method. A parametric study based on finite-element method simulations shows that considering the material anisotropy can significantly improve analysis accuracy (similar to 25 times higher than the theories neglecting the material anisotropy). These expressions maintain accuracy across almost the whole working voltage range (up to 96% of collapse voltages) and a wide dimension range (diameter-to-thickness ratios of 20-80 with gap-to-thickness ratios of <= 2). Furthermore, their utility in practical applications is well verified using numerical results based on more realistic boundary conditions and experimental results of CMUT chips. Finally, we demonstrate that the high accuracy of these expressions at thickness-comparable deflection results from the extended applicable deflection range of the CLTP theory when it is used for electrostatically actuated microplates.