OS-V: 0310 Deep Simply-Supported Beam Periodic Forced Vibration Response
Test 5P OptiStruct is used to investigate the Peak Displacement in the y-direction and extreme fiber bending stress 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 the end A. In addition, the displacements in y and z direction are constrained at end B. A steady-state periodic forced vibration F = F_{0} (sin ωt-sin 3ωt) is induced in the y-direction. (F_{0} = 10^{6} N/m uniformly distributed, ω = 2ωf, f = 20 Hz). For modal analysis solution, a damping ratio of 0.02 is applied in all 16 modes and for direct solution, Rayleigh damping factor α_{1} = 5.36 and α2 = 7.46×10^{-5} are given.
- Material Properties
- Value
- Young’s Modulus
- 200 × 10^{9} N/m^{2}
- Poisson’s Ratio
- 0.3
- Density
- 8000 kg/m^{3}
Frequency Response Summary
- f*
- Closed form solution
Peak Displacement (mm) | Peak Stress (N/mm^{2}) | |
---|---|---|
Reference Solution | 0.951 | 17.10 |
HOE: | ||
Direct Solution | 0.982 | 17.367 |
Normalized | 0.968431772 | 0.984626015 |
Modal Solution | 0.982 | 17.369 |
Normalized | 0.968431772 | 0.984512637 |
LOE: | ||
Direct Solution | 1 | 19.6 |
Normalized | 0.951 | 0.87244898 |
Modal Solution | 1 | 0.951 |
Normalized | 19.6 | 0.87244898 |
Reference
NAFEMS R0016 - Selected Benchmarks for Forced Vibration, J Maguire, D J, Dawswell, L Gould 1989