Timoshenko 和Euler 懸臂梁本身及帶額外微小質量在流體環境中共振頻及頻率飄移之比較

Abstract

This thesis is primarily based vibration model of Timoshenko beam in viscous fluid. To compare the vibration model with the vibration behavior of Euler beam in viscous fluid by the size, fluid type and modal order. In the end of the comparison, the added mass effect of two theoretical frequency shifts is compared. This thesis firstly introduces the relevant reference. 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 Euler beam theory and Timoshenko beam theory to obtain the frequency response function and the frequency response function which affected by the added mass after fluid-structure interaction. Ultimately, 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, different fluids, and the different modal orders. Finally, we can find out the added mass effect of resonant frequency which vibrates in the fluid environment of the two theories by the numerical results. Sensors often do measurements in the fluid environment. Because the effect of the frequency is smaller when the fluid acting on the structure, and the differences of Timoshenko beam theory and Euler beam theory become more obvious in high mode. The numerical results in this paper present that the difference in 8th mode is up to 65% when L/ h