Internal resonance based sensing in non-contact atomic force microscopy

In this letter, the nonlinear dynamics of a non-uniform micro-cantilever for atomic force microscopy is investigated numerically for a non-contact mode of operation. A step-like heterogeneity in the cantilever longitudinal direction yields conditions for both 3:1 and 2:1 internal resonances that govern quasiperiodic energy transfer between the first and second structural bending modes. Thus, quasiperiodic micro-cantilever response can enable multiple function sensing, and possible increased accuracy of time-varying forces via single frequency base excitation.