Nonlinear vibrations of the immersed dagger-shaped atomic force microscope cantilever in different liquids studied by experimental and theoretical methods

In this paper, the nonlinear dynamic behavior of an immersed dagger-shaped atomic force microscope cantilever in different liquids has been investigated for the first time. The Timoshenko beam theory, which considers rotatory inertia and shear deformation effects, has been used for modeling the cantilever. The nonlinear tip-sample interaction force has been modeled by using the Hertzian contact theory. Water, methanol, acetone, and carbon tetrachloride are considered as the immersion environments. In most cases, the softening behavior has been observed for the cantilever. The resonant frequency is found to decrease with an increase in the liquid viscosity. The experimental results have been compared with the theoretical predictions and are found to be in good agreement.