Table 1 Eigenvalues for a clamped-clamped uniform beam of square section, with thickness d =1 and length L =40
From: Component-based reduced basis for parametrized symmetric eigenproblems
λ 1 | λ 2 | λ 3 | λ 4 | |
|---|---|---|---|---|
Euler Bernoulli | 1.6294e-05 | 1.2381e-04 | 4.7583e-04 | 1.3003e-03 |
Timoshenko | 1.6204e-05 | 1.2224e-04 | 4.6524e-04 | 1.2560e-03 |
Global FEM | 1.6612e-05 | 1.2489e-04 | 4.7327e-04 | 1.2708e-03 |
SCRBE n A,p=108 | 1.6612e-05 | 1.2489e-04 | 4.7327e-04 | 1.2708e-03 |
SCRBE n A,p=20 | 1.6612e-05 | 1.2489e-04 | 4.7327e-04 | 1.2708e-03 |
\(\widetilde \Delta \) | 1.4418e-06 | 2.0695e-07 | 7.9612e-08 | 9.6913e-08 |
\(\widehat \Delta \) | 5.5488e-03 | 7.3845e-03 | 8.4207e-03 | 7.4811e-03 |
λ 5 | λ 6 | λ 7 | λ 8 | |
Euler Bernoulli | — | 2.9016e-03 | 5.6603e-03 | — |
Timoshenko | — | 2.7622e-03 | 5.2991e-03 | — |
Global FEM | 2.0732e-03 | 2.7775e-03 | 5.2916e-03 | 6.1912e-03 |
SCRBE n A,p=108 | 2.0732e-03 | 2.7775e-03 | 5.2916e-03 | 6.1912e-03 |
SCRBE n A,p=20 | 2.0732e-03 | 2.7775e-03 | 5.2916e-03 | 6.1912e-03 |
\(\widetilde \Delta \) | 5.4576e-09 | 4.1418e-07 | 1.0262e-06 | 8.8249e-09 |
\(\widehat \Delta \) | 3.3180e-02 | 8.3262e-03 | 8.9995e-03 | 4.7761e-03 |