Application of added mass concept of bending vibration to the design of a level-switch sensor

초록

This paper deals with the added mass of fluid around a cantilever rod vibrating transversely. This study is necessary to design a level switch sensor because its sensitivity depends on the change of the natural frequency in the presence of added mass effect. We considered solid and hollow cross-sections of elliptic and rectangular shapes with various aspect ratios and thicknesses. Stream function and velocity potential were obtained theoretically and numerically in the fluid adjacent to the rod, and the results yielded the added mass effect on the natural frequency of the bending vibration of the rod. After verifying numerical scheme by comparing its result with analytical one for a circular cross-section, we calculated numerically the effect of the added mass of fluid on the change of the natural frequency of a cantilever rod with various cross-sectional shapes. Experiments of modal testing support the calculated results. We showed the proportional relation of the sensor's sensitivity with the added mass effect and thus with the aspect ratio and thinness of the cross-section. The results of this study can be used to design the cross-sectional shape of the sensor to increase or decrease the sensitivity.