# 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.

## 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 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.

The material properties are:
Material Properties
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) 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

## Model Files

The model files used in this problem include:
• Test5TPBEAMLD.fem
• Test5TPBEAMLM.fem
• Test5TPBEAMD.fem
• Test5TPBEAMM.fem

## Reference

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