v2.02.101 SDLL101 - Vibration of a beam with pre-stress

Summary:

This flat problem consists in looking for the vibration frequencies of a mechanical structure composed of a slender girder, of circular cross section, under recessed and sliding tension. This Structural Mechanics test corresponds to a dynamic analysis of a linear model with linear behavior. This test includes two models.

In the first modeling, we test the Timoshenko beam element subjected to prestress, the calculation of the geometric rigidity and the calculation of the natural frequencies by the Lanczos method. In the second modeling, we test the Euler-Bernouilli beam element subjected to prestress, the calculation of the geometric rigidity and the calculation of the natural frequencies by the Bathe and Wilson method.

The results obtained are in good agreement with the results of guide VPCS. An upward shift in vibration frequencies is noted when the prestress in the beam increases.

• 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. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. Summary of results