Master’s Dissertation

StructuralMechanics

&Engineering

Acoustics

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STRUCTURE-ACOUSTIC ANALYSISUSING BEM/FEM;IMPLEMENTATION IN MATLAB

Structural Mechanics, LTH, Lund University, Box 118, SE-221 00 Lund, Sweden.Homepage: http://www.byggmek.lth.se

Structural Mechanics

Engineering Acoustics, LTH, Lund University, Box 118, SE-221 00 Lund, Sweden.Homepage: http://www.akustik.lth.se

For information, address:

Copyright © 2001 by Structural Mechanics & Engineering Acoustics, LTH, Sweden.Printed by KFS i Lund AB, Lund, Sweden, May 2001.

ISRN LUTVDG/TVSM--01/5107--SE (1-100)ISSN 0281-6679

Master’s Dissertation by

FREDRIK HOLMSTRÖM

Supervisors

PETER DAVIDSSON,Structural Mechanics

STRUCTURE-ACOUSTIC ANALYSIS

USING BEM/FEM;

IMPLEMENTATION IN MATLAB

JONAS BRUNSKOG,Engineering Acoustics

Engineering AcousticsISRN LUTVDG/TVBA--01/5029--SE (1-100)

ISSN 0281-8477

Detta är en tom sida!

Abstract

This master dissertation describes the process of implementing a couplingbetween the boundary element method (BEM) and the finite elementmethod (FEM) for three dimensional time harmonic structure-acousticmodels in CALFEM, which is a finite element toolbox to MATLAB.Since no boundary elements earlier have been represented in CALFEMthe development and implementation of constant and linear boundaryelements is also described in this thesis. To verify the correctness of theimplemented functions and to show how they are used three model ex-amples are performed: one using only BEM, and two structure-acoustics.

Keywords: BEM, FEM, Coupled, CALFEM, Vibro-Acoustics, Acous-tics, Implementation.

Cover Picture: Sound pressure level on vibrating plate.

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Preface

This master dissertation has been performed at the Division of StructuralMechanics and the Division of Engineering Acoustics, Lund University,during the autumn and spring term of year 2000/2001.

Supervisors for this work have been Eng. Lic. Jonas Brunskog andM. Sc. Peter Davidsson. I would like to express my gratitude for theirsupport, during times of both success and frustration. I would also liketo thank the personal at Structural Mechanics and at Building Acoustics,that have been involved in my work.

Finally, Andreas, Bjorn, Anders, and Peter deserves a thank, for keep-ing the spirit up in the ”master’s dissertation room”.

Lund, May 2001

Fredrik Holmstrom

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Summary

The purpose of this master dissertation is to implement BEM (������������ �� ���) and a coupling between BEM and FEM (���� � ����� �� ���) in CALFEM (a FEM toolbox to MATLAB) for structure-acoustic models.

Two different boundary elements, which formulations are based on theHelmholtz integral equation, has been developed: a one node constant,and a four node linear. Both elements are quadrilateral and can take anyorientation in the three dimensional space.

The linear boundary element can be coupled with two different fournode finite elements: a plate element with 12 degrees of freedom, and ashell element with 24 degrees of freedom.

Since BEM and coupled BEM/FEM problems, modelled with func-tions developed in this dissertation, can be very time consuming, the mostimportant future improvement is to construct time reducing measures.

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