OS-V: 0310 Deep Simply-Supported Beam Periodic Forced Vibration Response

Test 5P OptiStruct is used to investigate the Peak Displacement in y-direction and extreme fiber bending stress at the mid-span node.

図 1. FE Model with Boundary Conditions and Loadcases

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=F0 (sin ωt-sin 3ωt) is induced in the y-direction. (F0=106 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 α1=5.36 and α2=7.46×10-5 are given.

The material properties are:
Material Properties
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)
Reference Solution 0.951 17.10
Direct Solution 0.982 17.367
Normalized 0.968431772 0.984626015
Modal Solution 0.982 17.369
Normalized 0.968431772 0.984512637
Direct Solution 1 19.6
Normalized 0.951 0.87244898
Modal Solution 1 0.951
Normalized 19.6 0.87244898

Model Files


The model files used in this problem include:
  • Test5PPBEAMLD.fem
  • Test5PPBEAMLM.fem
  • Test5PPBEAMD.fem
  • Test5PPBEAMM.fem


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