Product: ABAQUS/Standard
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.
Eigenvalue extraction for a system with a symmetric stiffness matrix and multi-point constraints, selective modal recovery, full modal recover, and import.
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.
The eigenvalues obtained for both the AMS and Lanczos procedures are identical.
Eigenvalue extraction for a model with one element using the AMS eigensolver.
Preloading of a single C3D8 element.
Frequency extraction of the import model using the AMS eigensolver.
Constraints with Lagrange multipliers and submodeling, mode-based steady-state dynamic restart, and selective modal recovery.
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.
In the following table the frequency extraction step results obtained by the Lanczos and AMS eigensolvers are compared.
Full analysis using the AMS eigensolver.
Mode-based steady-state dynamic analysis restarted from the end of the frequency step.
Frequency extraction and mode-based steady-state dynamic analysis of a submodel driven entirely from the original model.
Coupled temperature-displacement steps, hybrid Bernoulli and Timoshenko beams, full modal recovery, and mode-based steady-state dynamic analysis.
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.
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.
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.
The following table shows the comparison of eigenfrequencies obtained by the Lanczos and AMS eigensolvers.
| Mode | Lanczos | AMS |
|---|---|---|
| 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 |
Axisymmetric tire model.
Three-dimensional tire model.
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.
The following table shows the comparison of eigenfrequencies obtained by the Lanczos and AMS eigensolvers.
Original model preloaded statically.
Solution-mapped model with further preloading and frequency extraction using the AMS eigensolver.
Material orientations, nodal transformations, initial conditions, selective modal recovery, and full modal recovery.
Relatively small problems with simple topologies constructed for testing the features mentioned above.
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%.
Model with material orientations and initial conditions.
Model with nodal transformations.
Models of simple topology to test the accuracy of residual modes using the AMS eigensolver.
The following table compares the eigenmodes obtained using the Lanczos and AMS eigensolvers.
| Residual | Mode | Lanczos | AMS |
|---|---|---|---|
| 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.
Three-dimensional model with residual modes, AMS, and full modal recovery.
Three-dimensional model with residual modes and Lanczos.
Two-dimensional model with residual modes, AMS, and selective modal recovery.
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.
Model with material motion.
Model with section distributions and SAXA12 elements.