Finite Element Study of Plane Wave Acoustic Phenomena in Ducts

MA-Thesis / Master von Juan Betts

Abstract:

This thesis studied the finite element modeling of plane wave acoustic phenomena in ducts. The study looked into finite element factors such as shape functions, mesh refinement, and element distortion.

The study concluded that the higher order shape function eight-node quadrilateral element gave considerably better results than lower order shape function four-node quadrilateral element. The eight-node element converged much faster to the analytical solution than the four-node element. The average error, taking all the cases in consideration, for the four-node element was around 30 % for a mesh refinement of about 14 elements per wavelength at 100 Hz frequency. The eight-node element in the other hand had average absolute errors of less than 1% under the same conditions.

This section also found that the eight-node element was substantially more resistant to solution deterioration due to element distortion than the four-node element.

For example distorting the four-node element up to 60° degrees usually increased errors very rapidly to above 100 % errors. The eight-node element on the other hand usually produced errors of less than 5 % for the same level of distortion.

The study showed that the type of boundary condition used had a significant effect on the solution accuracy. The study demonstrated that the effect of the natural boundary conditions was more global. Meeting this kind of boundary condition through mesh convergence produced accurate results throughout the duct.

Table of Contents:

1.	Introduction	1
1.1	Purpose and Methods	1
1.2	Literature Review	2
2.	Theoretical Analysis	4
2.1	Acoustics Fundamentals	4
2.2	Analytical Solutions	11
2.3	Finite Element Method	16
3.	Results & Discussion	22
3.1	Finite Element Mesh Refinement Analysis	23
3.2	Finite Element Distortion Analysis	37
3.3	Finite Element Mesh Refinement Analysis Revisited	47
4.	Conclusions & Recommendations	50
5.	Appendix A	52
6.	Appendix B	63
8.	References	68
9.	Vita	69