Vibration analysis of scanning thermal microscope probe nanomachining using Timoshenko beam theory

In this paper, the effect of thermal vibration on the resonant frequency of transverse vibration of scanning thermal microscope (SThM) cantilever probe is analyzed using the Timoshenko beam theory, including the effects of rotary inertia and shear deformation. The thermal vibration effect can be considered as an axial force and is dependent of temperature distribution of the probe. In this analysis, the temperature is assumed to be distributed in accordance with the constant, linear, and quadratic models along the probe length. The Rayleigh–Ritz method is used to solve the vibration problem of the probe. The numerical results show that the frequency obtained with the constant model is the highest, while it is the lowest for the quadratic model. The frequency of vibration modes of the probe increases with increasing the temperature of the probe. As the ratio of probe length to its thickness increases, the frequency of vibration modes decreases. In addition, the effects of rotary inertia and shear deformation on the frequency are significant, especially in higher order modes and smaller values of the ratio of the probe length to its thickness.