v2.01.027 SDLD27 - Spring mass system with 8 degrees of freedom with non-proportional viscous damper (modal analysis)

Summary:

This two-dimensional problem consists in looking for the frequencies, vibration modes and damping of a mechanical structure composed of masses, springs and viscous dampers. This Structural Mechanics test case corresponds to a dynamic analysis of a discrete model with linear behavior.

This test allows a complete validation of the discrete modeling options for stiffness, viscous damping, and mass (without finite elements) offered by the AFFE_CARA_ELEM command. Five different models are proposed: the modeling of discrete elements is either translational or translation/rotating and is written either in global coordinate system or in local coordinate system. In addition, various functionalities of the commands CALC_MODES (search for eigenvalues) and NORME_MODE (definition of the norm of an eigenvector) are tested for this quadratic problem.

This test refers to test VPCS, but it has been modified. In fact, the test orients the mechanical system on an axis \(\mathrm{3y}\mathrm{=}\mathrm{4x}\), which makes it possible to validate the entry of data in a local coordinate system. The results obtained are in good agreement with the reference results.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
  • 1.4. Initial conditions
• 2. Reference solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Uncertainty about the solution
  • 2.4. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
  • 3.4. Contents of the results file
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
  • 4.4. Contents of the results file
• 5. C modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
  • 5.4. Contents of the results file
• 6. D modeling
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of the mesh
  • 6.3. Contents of the results file
  • 6.4. Tested sizes and results
  • 6.5. Contents of the results file
• 7. E modeling
  • 7.1. Characteristics of modeling
  • 7.2. Characteristics of the mesh
  • 7.3. Tested sizes and results
  • 7.4. Contents of the results file
• 8. F modeling
  • 8.1. Characteristics of modeling
  • 8.2. Characteristics of the mesh
  • 8.3. Tested sizes and results
  • 8.4. Contents of the results file
• 9. Summary of results