FREQUENCY AND SENSITIVITY ANALYSIS OF ATOMIC FORCE MICROSCOPE (AFM) CANTILEVER CONSIDERING COUPLED FLEXURAL-TORSIONAL VIBRATIONS

Frequency analysis and modal sensitivity of an atomic force microscope (AFM) cantilever is presented in this paper. Closed-form expressions for frequency equation and sensitivity of vibration modes are derived for the tip-cantilever system as the cantilever undergoes coupled lateral-vertical bending with torsional vibration. In this work, the effects of the sample surface contact stiffness and the cantilever to tip lengths ratio on resonant frequencies and sensitivities are assessed. The results show that the resonant frequency is constant in low and high values of the normal and lateral contact stiffnesses and there is a shift of frequency in a specific value of stiffness. Also, in comparison with the values of normal contact stiffness, frequency shift, due to the tip-sample interaction, occurs in lower values of lateral contact stiffness. In the low values of contact stiffnesses, the lower-order vibration modes are more sensitive than the higher-order modes. The situation is completely reversed in very high contact stiffnesses. In addition the resonant frequencies are more sensitive to the variation of lateral contact stiffness with respect to the variation of normal contact stiffness.