v2.02.004 SDLL04 - Slender beam on two supports, coupled to a mass-spring system

Summary:

This flat problem consists in looking for the vibration frequencies of a mechanical structure composed of a built-in girder-slide and a mass connected to the beam by a spring. The spring stiffness and the mass depend on a variable parameter, which will make it possible to highlight the displacement of the natural frequencies for a small disturbance in the model. This Structural Mechanics test corresponds to a dynamic analysis of a linear model with linear behavior. It includes a single model.

This problem makes it possible to test the Timoshenko beam element in bending, the calculation of natural frequencies by the method of inverse iterations and by the Lanczos method, the discrete elastic connection between a point mass and a node of a beam.

The results obtained are in good agreement with the results given in guide VPCS. We can clearly observe the splitting of natural frequencies induced by the disturbance of the initial model (slender beam on two supports).

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
  • 1.4. Initial conditions
• 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. Summary of results