v2.02.009 SDLL09 - Vibration of a slender beam of variable rectangular cross section (freestanding)

Summary:

This flat problem consists in looking for the vibration frequencies of a free embedded beam with a rectangular variable cross section. This test includes a single modeling.

The variation in the cross section of the beam is either homothetic or non-homothetic. The characteristics of the cross section of the beam are given according to the cells in two different ways:

• section and inertia,

• height and width.

This problem therefore makes it possible to test the beam element with a variable cross section for a prismatic structure as well as the calculation of vibration frequencies by reverse iterations. Moreover, in operator AFFE_CARA_ELEM, we test the persistence of certain keywords.

The results obtained are in good agreement with those given in guide VPCS.

• 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
• 4. Summary of results