Harmonic balance method for FEM analysis of fluid flow in a vibrating pipe

摘要

A numerical procedure for the analysis of non-Newtonian fluid flow in a longitudinally vibrating tube is developed. The formulation of the problem is presented in differential equation form and finite element model is developed leading to the first-order matrix differential equation. A special modification of the harmonic balance procedure is proposed for this non-linear problem. Numerical validation of the harmonic balance procedure was performed by comparison of the average mass flow rate with the results of direct time integration.