Vibration Analysis of Scanning Near-Field Optical Microscope Probe Using the Timoshenko Beam Model

Abstract

The flexural vibration frequency for a scanning near-field optical microscope (SNOM) fiber probe has been derived using the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, and a closed-form expression has been obtained. In the analysis, the effects of the normal contact stiffness and the ratio of different probe dimensions on the frequency were studied. The results show that increasing the ratio of probe length to radius increases the vibration frequency of mode 1. In addition, the resonant frequencies based on the Bernoulli–Euler beam theory and the Timoshenko beam theory are compared. When the contact stiffness is very large for the higher modes, the effects of shear deformation and rotary inertia on the frequency become significant. This observation that the Timoshenko beam theory is able to predict the frequencies of flexural vibrations of the higher modes with higher contact stiffness for the SNOM fiber probe.