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.

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 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
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) Time at Peak Displacement (sec) Peak Stress (N/mm2) Static Displacement (mm)
Reference Solution 1.043 0.0117 18.76 0.538
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
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


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