LAUSR

Abstract In this paper, the nonlinear forced vibration of a piezoelectrically driven micro/nano cantilever-based biosensor is investigated via couple stress theory. The origin of nonlinear equations is the curvature, which causes cubic nonlinearities in the differential equation. Due to the dimensions of the structure and its size-dependent behavior, the governing equation is derived based on couple stress theory. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scales method. Then, the amplitude of the response and the nonlinear resonance frequency based on the classical and couple stress theory are presented and the effect of the absorption of the biological layer on the frequency variation of the two theories is compared with each other. Also, to achieve high sensitivity resulting from optimal dimensions, the variation of beam frequency for various dimensions has been studied. Finally, by studying the bifurcation points and half-stable region, the jump phenomenon in amplitude caused by biologic layer absorption as a strategy for biological detection has been investigated and the results validated qualitatively with previous studies.