OS-V: 0450 Free Cylinder: Axisymmetric Vibration

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



Figure 1. FE Model with Boundary Conditions and Loadcases

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

Benchmark Model

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

The material properties are:
Property
Value
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

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis