0c3c9c2f-a287-43f3-ba78-cd3afc863e3320210204052031392wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON FLUID MECHANICS2224-347X1790-508710.37394/232013http://wseas.org/wseas/cms.action?id=40361420211420211610.37394/232013.2021.16https://wseas.org/wseas/cms.action?id=23282MohamedGaithMechanical Engineering Department Al-balqa’ Applied University P.o.box 710709, Amman (11171), JordanA cantilevered tapered slender pipe conveying an incompressible, inviscid fluid of one material is not a conserved system. For certain large fluid velocity, the pipe with uniform cross section would go unstable via flutter Hopf bifurcation. In this paper, the flow induced vibration for cantilever tapering pipe transporting a fluid is presented. Euler Bernoulli and Hamilton’s theories are applied to develop the mathematical model which will be solved using well known Galerkan’s procedure. 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