OS-V: 0330 Deep Simply-Supported Beam Transient Forced Vibration Response
Test 5T OptiStruct is used to investigate the Peak Displacement in y-direction, the time at the peak displacement, extreme fiber bending stress at undamped Natural Frequency and the Static displacement at the mid-span node.
図 1. FE Model with Boundary Conditions and Loadcases
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 suddenly applied step load F0 = 106 N/m is induced in the y-direction. For modal analysis solution, a damping ratio of 0.02 is applied in all 16 modes at a time step of 0.0001 secs and for direct solution, Rayleigh damping factor α1 = 5.36 and α2 = 7.46×10-5 at a time step of 0.0001 secs are given.
- Material Properties
- 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) | Time at Peak Displacement (sec) | Peak Stress (N/mm2) | Static Displacement (mm) | |
|---|---|---|---|---|
| Reference Solution | 1.043 | 0.0117 | 18.76 | 0.538 |
| HOE: | ||||
| Direct Solution | 1.036 | 0.0116 | 18.02 | 0.533 |
| Normalized | 1.006756757 | 1.00862069 | 1.041065483 | 1.009380863 |
| Modal Solution | 1.03 | 0.0115 | 17.99 | 0.533 |
| Normalized | 1.012621359 | 1.017391304 | 1.042801556 | 1.009380863 |
| LOE: | ||||
| Direct Solution | 0.94 | 0.0109 | 18.02 | 0.48 |
| Normalized | 1.109574468 | 1.073394495 | 1.041065483 | 1.120833333 |
| Modal Solution | 0.939 | 0.01109 | 17.92 | 0.48 |
| Normalized | 1.110756124 | 1.055004509 | 1.046875 | 1.120833333 |
Reference
NAFEMS R0016 - Selected Benchmarks for Forced Vibration, J Maguire, D J, Dawswell, L Gould 1989