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 arectangular cantilever immersed in a uid to surface stiness variations has been analyzedand a closed-form expression is derived. to represent this sensitivity, we use analyticalformulas for the vibrational resonant frequencies of a rectangular cantilever beam immersedin an inviscid uid. the eect of the surface contact stiness on both exural and torsionalsensitivities in a uid is investigated and compared with cases in which the cantileveroperates in air. the results show that in low surface stiness, the rst mode is the mostsensitive. as sample surface stiness is increased, higher resonant frequencies show a largershift, compared with lower resonant frequencies. in addition, comparison between modalsensitivities in air and uid shows that the resonance frequency shifts in air are greaterthan resonant frequency shifts in uid.