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Dynamic behavior of atomic force microscope cantilevers

Kangzhi Shen, University of Nebraska - Lincoln


The dynamic behavior of rectangular, dagger-shaped, V-shaped and triangular cantilevers in atomic force microscope (AFM) is investigated systematically. Firstly, a series of closed-form characteristic equations including the influence of the height of the tip, thickness of the beam, the contact position and the angle between the cantilever and the sample surface are derived for the rectangular cantilevers modeled as an Euler-Bernoulli beam. Using this analysis reasons for disagreement between experimental and theoretical results based on the traditional model are found. Secondly, a convergent power series, which is demonstrated to be more effective than finite element method (FEM), is employed to solve the eigenvalue problems of dagger-shaped, V-shaped and triangular cantilevers. The general behavior of these kinds of cantilevers is studied with respect to the geometry and the contact position. Furthermore, the designs of the cantilevers with the highest sensitivity to the contact stiffness are investigated. Thirdly, a tangential contact model is derived, by which the tangential contact stiffness is demonstrated to be strongly related to the friction factor and always less than the normal contact stiffness. In addition, a contact damping model is proposed, by which the damping observed in experiments can be reasonably analyzed. Finally, the nonlinear behavior of the rectangular cantilever with Hertzian contact is investigated. The nonlinear vibration can be analyzed in a way similar to the linear problem by using the effective stiffness method proposed. A modified harmonic balance method for Hertzian contact is developed, by which the general nonlinear modes and the characteristic equation are derived. Both softening and hardening phenomena are found for the contact at and near the end of the cantilever respectively. The results presented here will impact dynamic AFM measurements, especially those focused on mechanical properties. ^

Subject Area

Applied Mechanics|Engineering, Materials Science

Recommended Citation

Shen, Kangzhi, "Dynamic behavior of atomic force microscope cantilevers" (2005). ETD collection for University of Nebraska - Lincoln. AAI3186880.