Bifurcations and chaos in vibrating microcantilevers of tapping mode atomic force microscopy

We study the dynamics of a microcantilever in tapping mode atomic force microscopy when it is close to the sample surface and the van der Waals force has an important influence. Utilizing the averaging method, the extended version of the subharmonic Melnikov method and the homoclinic Melnikov method, we show that abundant bifurcation behavior and chaotic motions occur in vibrations of the microcantilever. In particular, in the subharmonic Melnikov analyses, a degenerate resonance is treated appropriately. Necessary computations for the subharmonic and homoclinic Melnikov methods are performed numerically. Numerical bifurcation analyses and numerical simulations are also given to demonstrate the theoretical results.