Mass Sensitivity of Nonuniform Microcantilever Beams

Microelectromechanical systems (MEMS) based cantilever beams have been widely used in various sensing applications. Previous studies have aimed at increasing the sensitivity of biosensors by reducing the size of cantilever beams to nanoscale. However, the influence of nonuniform cantilever beams on mass sensitivity has rarely been investigated. In this paper, we discuss the mass sensitivity with respect to linear and nonlinear response of nonuniform cantilever beam with linear and quartic variation in width. To do the analysis, we use the nonlinear Euler–Bernoulli beam equation with harmonic forcing. Subsequently, we derive the mode shape corresponding to linear, undamped, free vibration case for different types of beams with a tip mass at the end. After applying the boundary conditions, we obtain the resonance frequencies corresponding to various magnitudes of tip mass for different kinds of beams. To do the nonlinear analysis, we use the Galerkin approximation and the method of multiple scales (MMS). Analysis of linear response indicates that the nondimensional mass sensitivity increases considerably by changing the planar geometry of the beam as compared to uniform beam. At the same time, sensitivity further increases when the nonuniform beam is actuated in higher modes. Similarly, the frequency shift of peak amplitude of nonlinear response for a given nondimensional tip mass increases exponentially and decreases quadratically with tapering parameter, α, for diverging and converging nonuniform beam with quartic variation in width, respectively. For the converging beam, we also found an interesting monotonically decreasing and increasing behavior of mass sensitivity with tapering parameter α giving an extremum point at $α=0.5$⁠. Overall analysis indicates a potential application of the nonuniform beams with quartic converging width for biomass sensor.