v2.04.100 SDLV100 - Vibration of a slender beam of variable rectangular cross section (freestanding)

Summary:

The structure studied is a free embedded steel beam with a variable rectangular cross section modelled by solid elements. We are interested in its natural frequencies during bending. The same problem is treated in beam modeling in test case SDLL09.

This problem makes it possible to test volume elements MECA_HEXA20 and MECA_PENTA15 in modal analysis. It also allows you to test option MASS_MECA_DIAG for calculating diagonalized mass matrices for volume models.

The reference solution is a numerical solution obtained using the finite element calculation code SAMCEF for similar models. The results obtained are also in good agreement with the semi-analytical results given in guide VPCS.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Properties of steel
  • 1.3. Boundary conditions and loads
• 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 values
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested values
• 5. Summary of results