Critical flow velocity of fluid-conveying magneto-electro-elastic pipe resting on an elastic foundation

The paper deals with the predicting critical flow velocity of a fluid-conveying magneto-electro-elastic pipe resting on a Winkler-like elastic foundation. Taking into account the Timoshenko beam theory, the constitutive law of magneto-electro-elastic materials and Maxwell's theory, the Hamilton's principle is applied for deducing the governing equations and corresponding boundary conditions of fluid-conveying magneto-electro-elastic pipes resting on the Winkler-like elastic foundation. The closed-form solutions of the critical flow velocity are obtained for fluid-conveying magneto-electro-elastic pipes with clamped-clamped and pinned-pinned ends, and can serve as benchmarks for any future numerical results. The effects of shear deformation, Winkler-like foundation and the magnetic and voltage potentials applied in magneto-electro-elastic pipes on the critical flow velocity are discussed in detail. Results show that the magnetic and voltage potentials have a significant effect on the critical flow velocities and therefore can be used to control the critical flow velocity by choosing some appropriate values of magnetic and electric potentials.