1 On the spurious eigenvalues for a concentric sphere in BIEM Reporter : Shang-Kai Kao Ying-Te Lee , Jia-Wei Lee and Jeng-Tzong C hen Date : 2008/11/28-29 The 32 nd National Conference on Theoretical and Applied Mechanics National Taiwan Ocean University MSVLAB Department of Harbor and River Engineering
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On the spurious eigenvalues for a concentric sphere in BIEM
The 32 nd National Conference on Theoretical and Applied Mechanics. On the spurious eigenvalues for a concentric sphere in BIEM. Reporter : Shang-Kai Kao Ying-Te Lee , Jia-Wei Lee and Jeng-Tzong Chen Date : 2008/11/28-29. National Taiwan Ocean University MSVLAB - PowerPoint PPT Presentation
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1
On the spurious eigenvalues for a concentric sphere in
BIEMReporter: Shang-Kai Kao
Ying-Te Lee , Jia-Wei Lee and Jeng-Tzong Chen
Date: 2008/11/28-29
The 32nd National Conference on Theoretical and Applied Mechanics
National Taiwan Ocean University
MSVLABDepartment of Harbor and River Engineering
2
Outline• Introduction
• Problem statement
• Mathematical analysis
• Numerical example
• Conclusions
3
Outline• Introduction
• Problem statement
• Mathematical analysis
• Numerical example
• Conclusions
4
Motivation
• 1-D
real-part BEM, CTAM31
• 2-D
Journal of Sound and Vibration, 2002
doubly-connected membrane, CTAM31
• 3-D
Computational Mechanics, 2002
5
BIEM and Null-field Integral Equation
Interior problem Exterior problem
cD
D D
x
xx
xcD
x x
Degenerate (separate) formDegenerate (separate) form
4 ( ) ( , ) ( ) ( ) ( , ) ( ) ( ),B B
u x T s x u s dB s U s x t s dB s x D 2 ( ) . . . ( , ) ( ) ( ) . . . ( , ) ( ) ( ),
B Bu x C PV T s x u s dB s R PV U s x t s dB s x B