Frequency extraction using the AMS eigensolver

This problem contains basic test cases for one or more Abaqus elements and features.

The tests in this section verify the frequency extraction procedure using the AMS eigensolver in Abaqus/Standard by comparing the results with those obtained by the Lanczos eigensolver.

This page discusses:

ProductsAbaqus/Standard

One-element tests

Elements tested

CPE4

C3D8

Features tested

Eigenvalue extraction for a system with a symmetric stiffness matrix and multi-point constraints, selective modal recovery, full modal recover, and import.

Problem description

The two-dimensional model consists of a linear element of unit length. The nodes at one end (y = 0) are constrained, while the nodes at the other end are involved in a LINK MPC. The eigenvalue extraction is performed for the undeformed configuration. The three-dimensional model consists of a single linear element and is mainly used for testing the import feature.

Results and discussion

The eigenvalues obtained for both the AMS and Lanczos procedures are identical.

Input files

ams_1cpe4.inp

Eigenvalue extraction for a model with one element using the AMS eigensolver.

ams_import0.inp

Preloading of a single C3D8 element.

ams_import.inp

Frequency extraction of the import model using the AMS eigensolver.

Model with various lagrange-multiplier constraints (contact, connectors, distributing couplings)

Elements tested

C3D8I

C3D8R

C3D10M

Features tested

Constraints with Lagrange multipliers and submodeling, mode-based steady-state dynamic restart, and selective modal recovery.

Problem description

The model consists of a semisphere pressed against a cube that is in contact with a rigid surface. The semisphere is also connected to the cube via four axial connectors.

In the preloading step the semisphere is pressed against the cube to establish contact. The load is applied at the reference node of the distributing coupling. In the second step the frequencies of the preloaded structure are extracted via the AMS procedure. Finally, the mode-based steady-state response is calculated in the third step using the results of the frequency extraction step. The results are compared with those obtained by the Lanczos eigensolver.

Results and discussion

In the following table the frequency extraction step results obtained by the Lanczos and AMS eigensolvers are compared.

ModeLanczosAMS
1 11.547 11.551
2 11.916 11.921
3 20.664 20.690
4 25.792 25.840
5 27.916 27.963
6 28.807 28.862
7 42.048 42.110
8 42.370 42.441

Model with coupled-temperature displacement

Elements tested

S8RT

B31H

B33H

B31

B33

Features tested

Coupled temperature-displacement steps, hybrid Bernoulli and Timoshenko beams, full modal recovery, and mode-based steady-state dynamic analysis.

Problem description

The model consists of two rectangular parallel plates connected via beams at each corner. The structure is preloaded by applying a heat flux at the center of the top plate. The linear response is analyzed in a mode-based steady-state dynamic step preceded by a frequency extraction step using the AMS solver.

Results and discussion

In the following table the frequency extraction step results obtained by the Lanczos and AMS eigensolvers are compared.

ModeLanczosAMS
1 14.743 14.745
2 14.743 14.748
3 15.296 15.301
4 17.158 17.164
5 29.476 29.505
6 38.684 38.749
7 38.684 38.773
8 52.778 53.009
9 63.201 63.545
10 67.253 67.621
11 67.253 67.641
12 70.055 70.555
13 87.080 87.166
14 88.789 89.594
15 88.789 89.720
16 88.818 90.292
17 91.946 92.735
18 92.877 93.825

Tire model with symmetric model generation and symmetric results transfer

Elements tested

CGAX3H

CGAX4H

SFMGAX1

Features tested

Eigenvalue extraction for a tire model with hybrid and/or cylindrical elements, axisymmetric model followed by symmetric model generation with symmetric results transfer, and full modal recovery.

Problem description

The axisymmetric tire is inflated and then transferred to a full three-dimensional configuration. Subsequently, the rigid surface is brought in contact with the full tire, obtaining the footprint. Finally, the linear response is analyzed by performing a frequency extraction using the AMS eigensolver followed by a mode-based steady-state dynamic step.

Results and discussion

The following table shows the comparison of eigenfrequencies obtained by the Lanczos and AMS eigensolvers.

ModeLanczosAMS
1 47.552 47.590
2 48.992 49.042
3 54.391 54.445
4 56.749 56.795
5 77.582 77.743
6 82.153 82.265
7 85.123 85.268
8 85.553 85.694
9 98.554 98.802
10 103.73 104.06
11 112.37 112.77
12 116.90 117.47
13 118.64 119.08
14 119.71 120.04
15 124.68 125.18
16 130.75 131.43
17 132.16 132.60
18 136.05 136.61
19 137.41 138.03
20 138.30 139.02
21 140.35 140.97
22 140.58 141.23
23 143.88 144.66
24 144.98 145.75
25 148.05 148.99
26 152.60 153.74

Model with map solution

Elements tested

CPS3

Features tested

Solution mapping and selective modal recovery.

Problem description

The first model is subject to a static preload. The solution is mapped onto a second mode with different elements, and the structure is further loaded statically. Finally, the eigenvalues of the loaded structure are extracted via the AMS eigensolver.

Results and discussion

The following table shows the comparison of eigenfrequencies obtained by the Lanczos and AMS eigensolvers.

ModeLanczosAMS
1 14.925 14.926
2 43.614 43.617
3 48.566 48.571
4 95.490 95.540

Models with material orientations, nodal transformations, and initial conditions

Elements tested

C3D8

SFM3D4R

S4

S8R

Features tested

Material orientations, nodal transformations, initial conditions, selective modal recovery, and full modal recovery.

Problem description

Relatively small problems with simple topologies constructed for testing the features mentioned above.

Results and discussion

The eigenfrequencies obtained by the AMS and Lanczos eigensolvers are identical for the model with material orientations and initial conditions. The model with nodal transformations exhibits differences smaller than 1%.

Models with residual modes

Elements tested

CPE4R

C3D20R

Features tested

Residual modes, selective modal recovery, and full modal recovery.

Problem description

Models of simple topology to test the accuracy of residual modes using the AMS eigensolver.

Results and discussion

The following table compares the eigenmodes obtained using the Lanczos and AMS eigensolvers.

ResidualModeLanczosAMS
no 1 4992.3 4993.1
no 2 5430.0 5430.9
no 3 7340.8 7344.6
no 4 10875. 10877.
no 5 13716. 13724.
yes 6 25445. 24359.
yes 7 36445. 34198.
yes 8 40925. 35377.

The maximum displacement in the steady-state dynamic step at 13kHz is 1.949 units with the Lanczos procedure, versus 1.848 units with the AMS eigensolver.

Miscellaneous models

Elements tested

SAXA12

M3D4

Features tested

Motion of material through the mesh and section distributions.

Problem description

Models with simple topology to test the features mentioned above.

Results and discussion

The results are identical using both the Lanczos and AMS eigensolvers for the model with material motion. For the model with section distributions and SAXA12 elements the results differ slightly in the fifth eigenvalue, as shown in the table below.

ModeLanczosAMS
1 531.33 531.33
2 771.31 771.31
3 1017.6 1017.6
4 1129.4 1129.4
5 1217.0 1217.1
6 1639.2 1639.2
7 1754.1 1754.1
8 2275.6 2275.6
9 3382.0 3382.0
10 3490.5 3490.5
11 3556.7 3556.7
12 3994.9 3994.9