In this work, a new theoretical model for contact resonance atomic force microscopy, which incorporates the elastic dynamics of a long sensing tip is presented. The model is based on the Euler-Bernoulli beam theory and includes coupling effects from the two-beam structure, also known as an 'L-shaped' beam in the literature. Here, high-accuracy prediction of the sample stiffness, using several vibration modes with a relative error smaller than 10% for practical working ranges, is demonstrated. A discussion on the model's capability to predict the dynamic phenomena of eigenmode veering and crossing, as the force applied to the sample increases, is presented. The L-shaped beam model presented here is also applicable for structural applications such as: micro-electro-mechanical systems, energy harvesting, and unmanned aerial vehicle landing gear.
Keywords: atomic force microscopy; contact resonance; long elastic tip; nano-needle; qPlus sensor.
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