Sensitivity analysis of vibration modes of rectangular cantilever beams immersed in uid to surface sti nessvariations

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