v2.02.002 SDLL02 - Slender, freestanding, recessed beam, folded on itself

Summary:

This two-dimensional problem consists in looking for the frequencies and the modes of vibration of a mechanical structure, composed of a slender, free embedded beam and folded in on itself.

The problem posed has no physical significance. On the other hand, it makes it possible to validate the search for multiple natural frequencies of bending and the search for double modes in a sub-space of order 2.

In this test, three different models are carried out:

• in the first modeling, the boundary conditions are imposed using Lagrange parameters (command AFFE_CHAR_MECA) and the eigenvalues and vectors are calculated by the Lanczos method (command CALC_MODES, METHODE =” TRI_DIAG “under the keyword factor SOLVEUR_MODAL),

• in the second modeling, the boundary conditions are imposed by removing degrees of freedom in the mass and stiffness matrices (command AFFE_CHAR_CINE) and the eigenvectors and values are calculated by the Bathe and Wilson method (command CALC_MODES, METHODE =” JACOBI “under the keyword factor SOLVEUR_MODAL)

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark 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. notes
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
  • 4.4. notes
• 5. Summary of results