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).

Figure 1.

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 random forcing 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.

The material properties are:
Young’s Modulus
200 × 109 N/m2
Poisson’s Ratio
8000 kg/m3

Frequency Response Summary

The frequency of each targeted mode is normalized with the closed form solution.
Closed form solution
  Peak Displacement (mm) Peak Stress (N/mm2) Frequency (Hz)
Reference Solution 180.90 58516 42.65
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
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

Model Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem include:
  • Test5RPBEAMLD.fem
  • Test5RPBEAMLM.fem
  • Test5RPBEAMD.fem
  • Test5RPBEAMM.fem


NAFEMS R0016 - Selected Benchmarks for Forced Vibration, J Maguire, D J, Dawswell, L Gould 1989