Effect of surface viscosity on the vibration of microcantilevers

Using the theory of beam bending and the theory of surface rheology, the equation describing the effect of a surface viscous film on the vibration of an elastic microcantilever is derived. A generalized solution for the vibration of the microcantilever is obtained, which depends on the boundary conditions and the surface viscosity. There is a phase lag between the externally harmonic excitation and the microcantilever response due to the energy loss from surface flow. For small energy dissipation with negligible surface energy, the maximum energy loss occurs approximately at the natural frequencies of the microcantilever.