Improved Analytical Modeling of Membrane Large Deflection With Lateral Force for the Underwater CMUT Based on Von Kármán Equations

Abstract

This paper is to develop analytical models for the underwater capacitive micromachined ultrasonic transducer (CMUT) to understand its large deflection effect from the water pressure. To accurately model the displacement profile of the CMUT under the water pressure, Von Karman equations and the perturbation method are employed to calculate the membrane deformation from a uniform pressure. The equations for an annular-ring plate model are first applied to calculate the displacement profile of the uniform CMUT membrane. The lateral force due to the membrane elongation is considered in the proposed model, which is used to calculate the displacement profiles for both conventional and collapse mode CMUTs under different external pressures. When compared with finite-element method results, the proposed model can predict the displacement profiles of the conventional-mode CMUT under water pressure ranging from 0.8 to 4 MPa with an error of <1%. It can also estimate CMUT membrane that operates in collapse mode with an error in the deflection profile for <4.7% from 5 to 14 MPa. In addition, it is worth to mention that the proposed model can cover the small deflection scenarios but with relatively larger error under collapse mode.