Finite element analysis of stress stiffening effects in CMUTS

We use finite element analysis (FEA) to model capacitive micromachined ultrasonic transducer (CMUT) cells where stress stiffening affects static deflection, pull-in voltage, resonance frequency, and small-signal sensitivity. Determining the small-signal sensitivity is challenging because it requires a prestressed harmonic response analysis in which the geometric nonlinearities are activated during the static analysis to prestress the structure. The goal is a correct static operation point calculation for CMUT plates that exceed a static deflection-to-thickness ratio of 20%. Assuming only a small AC excitation, we use a linear but updated stiffness matrix to calculate the harmonic response. We achieve this by using a prestressed mode superposition harmonic response analysis, which uses the sum of factored mode shapes obtained from a nonlinear prestressed modal analysis. We test our FEA for two CMUTs, of which one operates in a more membrane-dominated regime. Comparisons to measurements demonstrate that only the FEA that accounts for stress stiffening features good agreement for both designs. Our FEA allows us to model CMUTs that operate in a more membrane-dominated regime.