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Frequency Analysis of a Sphere

Overview

The aim of this test case is to validate the following functions:

  • Calculation of eigenfrequencies

The simulation results of SimScale were compared to the numerical results in [SDLV401]. The meshes used in (A) and (B) were created with the parametrized-tetrahedralization-tool on the SimScale platform.

Import validation project into workspace

Geometry

FullSphereFreeFree-geometry

Geometry of the hollow cylinder

  • Sphere radius r = 0.01 m

Analysis type and Domain

Tool Type : CalculiX

Analysis Type : Frequency

Mesh and Element types :

Case Mesh type Number of nodes Element type
(A) linear tetrahedral 504 3D isoparametric
(B) quadratic tetrahedral 3130 3D isoparametric
FullSphereFreeFree-mesh

Mesh used for the SimScale case (A)

Simulation Setup

Material:

  • isotropic: E = 20 MPa, \(\nu\) = 0.3, \(\rho\) = 10000 kg/m³

Constraints:

  • the sphere is free, no constraints

Results

Comparison of the first, non-zero eigenfrequencies obtained with SimScale with the results presented in [SDLV401]. The Error was calculated with respect to [SDLV401_N].

Comparison of the eigenfrequencies in [Hz] obtained with first order elements
Mode [SDLV401_N] [SDLV401] SimScale case (A) Error (%)
1 2542.31 2542.31 2612.04 2.74
2 2543.31 2543.31 2616.36 2.87
3 2607.47 2607.47 2619.65 0.47
4 2608.47 2608.47 2621.93 0.52
5 2609.47 2609.47 2627.48 0.69
6 2740.95 2740.95 2722.00 -0.69
7 2741.95 2741.95 2725.04 -0.62
8 2742.95 2742.95 2729.05 -0.51
9 2763.13 2763.13 2729.24 -1.23
10 2764.13 2764.13 2732.64 -1.14
Comparison of the eigenfrequencies in [Hz] obtained with second order elements
Mode [SDLV401_N] [SDLV401] SimScale case (B) Error (%)
1 2470.35 2469.64 2469.48 -0.04
2 2470.35 2469.64 2469.50 -0.03
3 2471.01 2470.84 2469.54 -0.06
4 2471.01 2470.84 2469.54 -0.06
5 2471.01 2470.84 2469.55 -0.06
6 2612.96 2613.44 2612.71 -0.01
7 2612.96 2613.44 2612.75 -0.01
8 2614.30 2613.45 2612.76 -0.06
9 2614.30 2613.64 2612.78 -0.06
10 2614.30 2613.64 2612.81 -0.06

References

[SDLV401_N](1, 2, 3) Numerical reference computed with SAMCEF as stated in [SDLV401]
[SDLV401](1, 2, 3, 4, 5) SDLV401 - Sphère pleine libre-libre