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Effect of viscous axial loading on vibrating microcantilever sensors

In this paper we analyze the flexural dynamics of a microelectromechanical system cantilever immersed in a fluid medium by taking into account the effect of tangential viscous drag due to beam curvature. The latter appears as an additive nonlinear damping term in the equation of motion. The cantilever motion is described within the framework of the Euler–Bernoulli beam theory by using the normal mode representation. It is found that the tangential drag with beam curvature causes the cantilever oscillation frequency to depend on its amplitude. This effect is more pronounced for large aspect ratio cantilevers in high viscosity media. The implications of this for the interpretation of atomic force microscopy and biosensor data are discussed, and a method for correction is suggested.