OS-V: 0450 Free Cylinder: Axi-symmetric Vibration

Test No. FV41 A free cylinder with axi-symmetric vibration. OptiStruct is used to investigate the rigid body mode, close eigenvalues, and the coupling between axial, radial and circumferential behavior.



Figure 1.

Benchmark Model

The 1st order and 2nd order triangular axi-symmetric elements (CTAXI) are used to model the cylinder. The cylinder is unsupported.

The material properties are:
Young's Modulus
200 x 109 N/m2
Poisson's Ratio
0.3
Density
8000 kg/m3

Modal Analysis Results

Mode shapes predicted by OptiStruct.


Figure 2.
The frequency of each targeted mode is normalized with the NAFEMS closed form solution.
  Mode
  1 2 3 4 5 6
NAFEMS RBM 243.53 Hz 377.41 Hz 394.11 Hz 397.72 Hz 405.28 Hz
HOE (8×1) RBM 243.34 Hz 372.14 Hz 374.18 Hz 378.22 Hz 396.00 Hz
Normalized 1 1.000780801 1.014161337 1.053263135 1.051557295 1.023434343
HOE (16×3) RBM 243.46 Hz 377.15 Hz 393.2 Hz 394.6 Hz 400.97 Hz
Normalized 1 1.000287522 1.000689381 1.002314344 1.007906741 1.010748934
LOE (8×1) RBM 242.45 Hz 376.02 Hz 379.86 Hz 389.83 Hz 426.92 Hz
Normalized 1 1.004454527 1.003696612 1.037513821 1.020239592 0.949311346
LOE (16×3) RBM 243.28 Hz 377.69 Hz 391.42 Hz 395.54 Hz 423.00 Hz
Normalized 1 1.001027622 0.999258651 1.006872413 1.005511453 0.958108747

Model Files

The model files used in this example include:

<install_directory>/demos/hwsolvers/optistruct/verification
  • /FV41HOEC.fem
  • /FV41HOEF.fem
  • /FV41LOEC.fem
  • /FV41LOEF.fem

Reference

NAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish Enterprise Technology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.