Modelling of CMUTs with anisotropic plates

Traditionally, CMUTs are modelled using the isotropic plate equation and this leads to deviations between analytical calculations and FEM simulations. In this paper, the deflection profile and material parameters are calculated using the anisotropic plate equation. It is shown that the anisotropic calculations match perfectly with FEM while an isotropic approach causes up to 10% deviations in deflection profile. Furthermore, we show how commonly used analytic modelling methods such as static calculations of the pull-in voltage and dynamic modelling through an equivalent circuit representation can be adjusted to include the correct anisotropic behaviour by using an effective flexural rigidity. The anisotropic calculations are also compared to experimental data from actual CMUTs showing an error of maximum 3%.