Viscous damping on flexural mechanical resonators

• We derive a new analytical formula for the Q factor of flexural mechanical resonators.
• We carry on experimental measurements of the Q factor of several resonators.
• We discuss the validity of the prediction.
• We present a new model for the viscous damping on tuning forks.

A new analytical formula predicting the quality factor of a wide range of flexural mechanical resonators operating in a viscous fluid medium is presented. The formula is derived from a fluid analogy used in the single beam Euler–Bernoulli bending theory, and an extension to tuning forks is proposed. Comparisons with experimental data extracted from the literature are presented. New experiments have also been carried out on different kinds of resonators to investigate the pressure dependency of their quality factors in air. In both cases, very good agreement is obtained for resonator sizes ranging from micrometric to macroscopic sizes.