Acoustic damping on flexural mechanical resonators

Flexural resonators operated within a fluid are most of the time limited by viscous damping. Nonetheless, depending on the resonator geometry, significant acoustic damping has also to be considered. After reviewing the main theoretical approaches proposed in the literature to evaluate acoustic losses, we provide useful and simplified expressions to quantify their corresponding quality factor. Original results are obtained by extending well-known methods to different shapes. We also present numerical simulations and experiments to compare and assess the validity of our predictions, and show that analytical models combining both viscous and acoustic damping can give reliable values for the observed quality factors.