Abstract
A pseudo-spectral approach to 2D vibrational problems arising in linear elasticity is considered using differentiation matrices. The governing partial differential equations and associated boundary conditions on regular domains can be translated into matrix eigenvalue problems. Accurate results are obtained to the precision expected in spectral-type methods. However, we show that it is necessary to apply an additional "pole" condition to deal with the r=0 coordinate singularity arising in the case of a 2D disc.
| Original language | English |
|---|---|
| Pages (from-to) | 95-110 |
| Number of pages | 16 |
| Journal | Numerical Algorithms |
| Volume | 38 |
| Issue number | 1-3 |
| DOIs | |
| Publication status | Published - Mar 2005 |
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Application of the pseudo-spectral method to 2D eigenvalue problems in elasticity. / Talbot, C. J.; Crampton, A.
In: Numerical Algorithms, Vol. 38, No. 1-3, 03.2005, p. 95-110.Research output: Contribution to journal › Article
TY - JOUR
T1 - Application of the pseudo-spectral method to 2D eigenvalue problems in elasticity
AU - Talbot, C. J.
AU - Crampton, A.
PY - 2005/3
Y1 - 2005/3
N2 - A pseudo-spectral approach to 2D vibrational problems arising in linear elasticity is considered using differentiation matrices. The governing partial differential equations and associated boundary conditions on regular domains can be translated into matrix eigenvalue problems. Accurate results are obtained to the precision expected in spectral-type methods. However, we show that it is necessary to apply an additional "pole" condition to deal with the r=0 coordinate singularity arising in the case of a 2D disc.
AB - A pseudo-spectral approach to 2D vibrational problems arising in linear elasticity is considered using differentiation matrices. The governing partial differential equations and associated boundary conditions on regular domains can be translated into matrix eigenvalue problems. Accurate results are obtained to the precision expected in spectral-type methods. However, we show that it is necessary to apply an additional "pole" condition to deal with the r=0 coordinate singularity arising in the case of a 2D disc.
KW - Boundary value problems
KW - Collocation
KW - Differentiation matrices
KW - Elasticity
KW - Solid mechanics
KW - Spectral methods
UR - http://www.scopus.com/inward/record.url?scp=23944514603&partnerID=8YFLogxK
U2 - 10.1007/s11075-004-2860-5
DO - 10.1007/s11075-004-2860-5
M3 - Article
VL - 38
SP - 95
EP - 110
JO - Numerical Algorithms
JF - Numerical Algorithms
SN - 1017-1398
IS - 1-3
ER -