LAUSR

Abstract Dynamic modes of an Atomic Force Microscope (AFM) can be modeled as a cantilever beam excited near one or more resonant frequencies described by the Euler-Bernoulli PDE with additional damping and controlled excitation. The PDE is equivalent to a series of coupled nonlinear ODEs; each ODE defines its resonant frequency. Using the Krylov-Bogoliubov-Mitropolsky (KBM) averaging technique, these ODEs can be approximated by asymptotic amplitude-phase multi-resonant dynamics. We present the PDE with parameters estimated by AFM measurements, derive the asymptotic multi-resonant dynamics and discuss perspective nomenclature of AFM multi-resonant modes, their control, and implementation that extends single-resonant modes.