Timoshenko beam effects in lateral‐mode microcantilever‐based sensors in liquids

Recent experimental and analytical research has shown that higher in-fluid quality factors (Q) are achieved by actuating microcantilevers in the lateral flexural mode, especially for microcantilevers having larger width-to-length ratios. However, experimental results show that for these geometries the resonant characteristics predicted by the existing analytical models differ from the measurements. A recently developed analytical model to more accurately predict the resonant behaviour of these devices in viscous fluids is described. The model incorporates viscous fluid effects via a Stokes-type fluid resistance assumption and ‘Timoshenko beam’ effects (shear deformation and rotatory inertia). Unlike predictions based on Euler-Bernoulli beam theory, the new theoretical results for both resonant frequency and Q exhibit the same trends as seen in the experimental data for in-water measurements as the beam slenderness decreases. An analytical formula for Q is also presented to explicitly illustrate how Q depends on beam geometry and on beam and fluid properties. Beam thickness effects are also examined and indicate that the analytical results yields good numerical estimates of Q for the thinner (5 μm) specimens tested, but overestimate Q for the thicker (20 μm) specimens, thus suggesting that a more accurate fluid resistance model should be introduced in the future for the latter case.