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).

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 end A. In addition, the displacements in y and z direction are constrained at end B. A steady-state random force 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:
Property
Value
Young’s Modulus
200 × 109 N/m2
Poisson’s Ratio
0.3
Density
8000 kg/m3

Frequency Response Summary

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

Reference

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