The Finite Element Model of Vibroacoustical Characteristics of Pipe System Under Force Excitation by Oscillating Fluid Flow

Abstract

The finite element mathematical technique of vibroacoustical pipeline characteristics are developed. The technique allows calculations vibroacoustical characteristics of pipe with the axial line lying in one plane under force excitation by oscillating fluid flow. The technique is based on the solving differential equation system of interaction between solid and oscillating fluid in the pipeline. Solution was done for transient non-stationary nonlinear differential equation system. The weighted residual approximation with relations for a Galerkin finite element solutions were done. The boundary conditions for fluid is a parameter combination of complex pressure oscillation amplitude of pipeline inlet section, complex pressure oscillation amplitude of pipeline outlet section, complex velocity oscillation amplitude of pipeline inlet section, complex velocity oscillation amplitude of pipeline outlet section, load impedance, input impedance. The boundary conditions for solid is bonding of the pipeline. In this technique new seven node element were proposed. The new space-time single type elements based on Lagrange basis function. The single type of finite element are used for modeling vibroacoustical interaction between solid and oscillating fluid. Time response and amplitude spectrum of the pipeline vibration are resulted of these techniques. The mathematical technique computational coast is 3 orders less than available finite element techniques. The convergence estimate of experimental data and simulation results are made. The method is developed for pipeline diameter much smaller than acoustic wavelength in a fluid. It is actual for aircraft pipelines, pipes of power plants, mobile machines and pipes of stationary processing machines.