Beam model and three dimensional numerical simulations on suspended microchannel resonators

At the microscale level, the vibrational characteristics of microstructures have been widely applied on biochemical microchips, especially for bio-molecules detection. The vibrational mechanics and mechanism of microcantilever beams immersed in the fluids for detecting target bio-molecules carried in the fluids have been widely studied and realized in recent years. However, it is not the case for microcantilever beams containing fluids inside (called suspended microchannel resonators, SMR). In this paper, an 1-D beam model for SMR is proposed and the formula for prediction of resonant frequency and resonant frequency shift are derived. For verification of validity of the 1-D beam model, three dimensional finite element simulations using ANSYS are performed. The effects of relevant parameters, such as density and viscosity of the fluids, on the frequency response are investigated. A link between numerical simulations and mathematical modeling is established through an equivalence relation. Subsequently, a useful formula of the resonant frequency shift as a function of the mass variation and the viscosity of the contained fluid is derived. Good agreement between the numerical simulations and the experimental data is obtained and the physical mechanism is elucidated.