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

TL;DR

This paper presents an exact analytical solution for the forced vibration response of a cantilevered tube conveying fluid under harmonic excitation, improving accuracy over traditional methods.

Contribution

It introduces a Green's function-based analytical technique that yields exact solutions without eigenfunction expansion or infinite series.

Findings

Provides closed-form solutions for forced vibrations

Eliminates need for eigenfunctions and eigenvalues

Achieves higher accuracy than classical methods

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.