v2.04.302 SDLV302 — Modal analysis by substructuration: double-supported beam

Summary:

This test validates the modal analysis of a structure using the dynamic substructuring method. The structure studied is a double-supported beam that can be deformed by shear force.

It is modelled by hexahedral volume elements with 20 nodes (3D modeling).

Modal analysis is carried out by three methods:

• direct approach;

• Craig-Bampton dynamic substructuring approach;

• direct approach with proportional viscous damping.

A particular advantage of this test is the presence of linear relationships between several degrees of freedom.

The calculated natural frequencies are compared to values obtained analytically for a Timoshenko beam model deformable under shear force and taking into account the rotatory inertia of the sections.

• 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 A
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
• 4. B modeling
  • 4.1. Characteristics of B modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. C modeling
  • 5.1. Characteristics of C modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
• 6. D modeling
  • 6.1. Characteristics of modeling D
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
• 7. Summary of results