Effect of thermal vibrations on the resonant frequency of cantilever for scanning thermal microscopy nanomachining

Abstract

The effect of thermal vibrations on modal frequencies of flexural vibration for a scanning thermal microscope (SThM) cantilever probe has been evaluated using the Timoshenko beam model, including the effects of rotary inertia and shear deformation, and an analytical expression for the frequencies of vibration modes has been obtained. According to this analysis, the thermal vibration effect makes the probe stiffer and leads to an increasing frequency in the nanomachining process. This phenomenon may result in a rough machined surface of the materials. The resonant frequency of vibration modes decreases as the length-to-thickness ratio of the probe increases. The mode shape decreases with increasing the operating temperature in SThM machining. In addition, the results based on Euler beam and Timoshenko beam models are compared. It can be found that the Timoshenko beam model is able to predict the frequencies of flexural vibration of the higher modes for the SThM cantilever probe nanomachining.