Derivation of an Analytical Solution of a Forced Cantilevered Tube Conveying Fluid

Abstract

In this paper, an analytical technique is proposed to obtain the forced response of a cantilevered tube conveying fluid. By considering the pipe subjected to an arbitrary harmonic force, either distributed or concentrated, an analytical solution is found using the Green's function method. The closed-form solution obtained satisfies the differential equations governing the vibrating tube conveying fluid. The proposed method, which provides exact solutions, is more accurate than the classical eigenfunction expansion or Galerkin's method and eliminates the need for eigenfunctions, eigenvalues, or infinite series.