Superharmonic Solutions of Order (2,3) to a MEMS Governed the Motion of a TM-AFM Cantilever

The superharmonic solutions of a weakly nonlinear second order differential equation governed the dynamic behavior of a microcantilever based on TM (Tapping mode) AFM (Atomic force microscopy) are studied analytically by applying the method of multiple scales (MMS). The modulation equations of the amplitude and the phase are obtained. Steady state solutions, frequency response equations, the peak amplitudes with their locations and the approximate analytical expressions are obtained. The stability of the steady state solutions is given. Numerical solutions of the frequency response equations and their stability conditions are carried out for different values of the parameters in the equation. Results are presented in groups of figures. Finally, discussion and conclusion are given.