Sensitivity Analysis of Vibration modes of Rectangular Cantilever Beams Immersed in Fluid to Surface Stiffness Variations

In this paper, the sensitivity of flexural and torsional vibration modes of a rectangular cantilever immersed in a fluid to surface stiffness variations has been analyzed and a closed-form expression is derived. To represent this sensitivity, we use the analytical formulas for the vibrational resonant frequencies of a rectangular cantilever beam immersed in an inviscid fluid. The effect of the surface contact stiffness on both flexural and torsional sensitivities in a fluid is investigated and compared with the case that cantilever operates in the air. The results show that in the low surface stiffness, the first mode is the most sensitive mode. As the sample surface stiffness is increased, higher resonant frequencies show a larger shift as compared with lower resonant frequencies. In addition, comparison between modal sensitivities in air and fluid shows that the resonance frequency shifts in the air are greater than the resonant frequency shifts in the fluid.