v2.02.403 SDLL403 - Vibrations of a rotating pendulum

Summary

The field of application of this test is the modal analysis of structures. The structure studied is a pendulum rotating around a fixed axis and immersed in a field of gravity. The pendulum is itself articulated around an axis perpendicular to the axis of rotation and located at a certain distance from this one.

We are interested in the first six natural frequencies.

The interest of this test lies in the following aspects:

• modal analysis taking into account initial constraints (geometric stiffness)

• modal analysis taking into account centrifugal stiffness

• significant relative difference between two successive frequencies of the spectrum

Currently, taking into account centrifugal stiffening is only possible with volume elements. The element used is element HEXA20 and the Sorensen method is used to calculate the natural frequencies.

The first natural frequency is compared to an analytical reference. The following frequencies are compared to numerical values obtained by software independent of Code_Aster and using “beam” and “plane strain” models.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loading
  • 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
• 4. Summary of results