Comparisons of Resonant Frequency between Timoshenko and Euler Cantilever Beam Immersed in the Fluid Environments
Date Issued
2014
Date
2014
Author(s)
Ting, Shang-Yang
Abstract
This paper build the vibration model of Timoshenko beam in viscous fluid. To compare the behavior with the vibration model of Euler beam in viscous fluid by the size, order of modes, fluid environment and shear modulus.
Using the Green''s function to solve incompressible viscous fluid theorem of any cross-section, and to conclude hydrodynamic loading that fluid applied to the flat beam. After that, have the hydrodynamic functions coupled with the Timoshenko beam theory to obtain the frequency response function and the frequency response function which affected by the added mass after fluid-structure interaction.
The Timoshenko beam numerical results are verified with the physical behavior, the relationship between the two theories and the numerical results of the reference. The numerical results of the frequency response functions were compared the relationship to two theories in different sizes of beam, different density and viscosity of fluid environment, different shear modulus, and the different order of modes. When using the micro-cantilever sensors in the fluid environment for measurement, the difference between Timoshenko beam theory and Euler beam theory will be greater than the vacuum. In addition, if we want to get the better sensitivity, we need to measure in higher mode and use the thicker beam. At such times, using the Timoshenko beam theory which considers the shear deformation and the moment of inertia can make calculations more appropriate than Euler beam theory.
Subjects
微懸臂梁感測器
原子力顯微鏡
振動
頻率響應
Timoshenko梁理論
Euler梁理論
黏滯流體
Type
thesis
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