| Summary: | 博士 === 國立成功大學 === 機械工程學系碩博士班 === 96 === The objective of this dissertation is to study the vibration of Scanning Near-Field Optical Microscope (SNOM) probe including frequency, sensitivity, and interactive force, respectively, while the probe scans samples.
In the frequency analysis, the effect of interactive damping on the flexural vibration frequency for the SNOM’s probe based on the Timoshenko beam theory, with the effects of shear deformation and rotary inertia, has been analyzed. Besides, the effects of the contact stiffness, damping factor and the ratio of different probe dimensions on the damping vibration frequency were studied. The results show that increasing the ratio of probe length to radius increases the vibration frequency of first five modes. 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.
In the sensitivity analysis, the effect of interactive damping on the sensitivity of flexural and axial vibration modes of SNOM with a tapered optical fiber probe has been analyzed. The interaction of the SNOM probe with the sample surface is modeled by a combination of a spring and a dashed pot in the lateral direction and a similar combination in the axial direction. An approximate form for the sensitivities of both modes was derived by using the Rayleigh-Ritz method. The results show that the interactive damping will decrease the sensitivities of both flexural and axial vibration modes when the contact stiffness is low. The more the damping effect, the lower the sensitivities are. In addition, when the contact stiffness was low, the mode 1 of flexural sensitivity slightly increased as the tapered angle decreased, but the flexural sensitivity increased as the tapered angle increased in high modes. However, the axial sensitivity apparently decreased as the tapered angle decreased. When the contact stiffness became higher, the sensitivities of both flexural and axial vibration modes increased as the tapered angle increased.
In the interactive force, the conjugate gradient method of minimization with an adjoint equation is successfully applied to solve the inverse problem in estimating the shear or axial force between the tapered probe and sample during the scanning process SNOM. While knowing the available deflection at the tapered probe tip, the determination of the interaction force is regarded as an inverse vibration problem. In the estimating processes, no prior information on the functional form of the unknown quantity is required. The accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements of deflection at the tapered probe tip. Numerical results show that good estimations on the interaction shear force can be obtained for all the test cases considered in this study.
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