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.

Figure 1. FE Model with Boundary Conditions and Loadcases

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

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


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