OS-V: 0390 Deep Simply-Supported Beam Random Forced Vibration Response
Test 5R OptiStruct is used to investigate the Peak Displacement in y-direction and extreme fiber bending stress at undamped Natural Frequency (at the mid-span node).
Model Files
Benchmark Model
Timoshenko beam and Engineer’s beam elements are used to model the simply-supported beam which consists of 10 elements. The displacements in x, y, and z direction, as well as the rotation in x direction are fixed at end A. In addition, the displacements in y and z direction are constrained at end B. A steady-state random force with uniform power spectral density (of force) PSD = (106 N/m)2/Hz is induced in the y-direction. For modal analysis solution, a damping ratio of 0.02 is applied in all 16 modes and for direct solution, Rayleigh damping factor α1 = 5.36 and α2 = 7.46×10-5 are given.
- Property
- Value
- Young’s Modulus
- 200 × 109 N/m2
- Poisson’s Ratio
- 0.3
- Density
- 8000 kg/m3
Frequency Response Summary
f*
- Closed form solution
Peak Displacement (mm) | Peak Stress (N/mm2) | Frequency (Hz) | |
---|---|---|---|
Reference Solution | 180.90 | 58516 | 42.65 |
HOE: | |||
Direct Solution | 184.03 | 56999.67 | 43.14 |
Normalized | 0.982991903 | 1.026602435 | 0.988641632 |
Modal Solution | 183.93 | 56973.24 | 43.16 |
Normalized | 0.983526342 | 1.027078678 | 0.988183503 |
LOE: | |||
Direct Solution | 150.9 | 56917.35 | 45.34 |
Normalized | 1.198807157 | 1.028087218 | 0.94067049 |
Modal Solution | 151.4 | 57105.24 | 45.34 |
Normalized | 1.194848085 | 1.024704563 | 0.94067049 |
Reference
NAFEMS R0016 - Selected Benchmarks for Forced Vibration, J Maguire, D J, Dawswell, L Gould 1989