VM19

VM19
Random Vibration Analysis of a Deep Simply-Supported Beam

Overview

Reference: NAFEMS, Selected Benchmarks for Forced Vibration, Report prepared by W. S. Atking Engineering Sciences, April 1989, Test 5R.
Analysis Type(s):
Mode-frequency, Spectrum Analysis (ANTYPE = 8)
Element Type(s): 3D 2 node beam (BEAM188)
Input Listing: vm19.dat

Test Case

A deep simply-supported square beam of length , thickness t, and mass density m is subjected to random uniform force power spectral density. Determine the peak response PSD value.

Figure 25: Simply-Supported Beam Problem Sketch

Simply-Supported Beam Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 200 x 109 N/m2
υ = 0.3
m = 8000 Kg/m3
= 10. m
t = 2.0 m
PSD = (106 N/m)2 /Hz
Damping δ = 2%

Analysis Assumptions and Modeling Notes

Modal analysis is performed using Block-Lanczos eigensolver. A frequency range of .1 Hz to 70 Hz was used as an approximation of the white noise PSD forcing function frequency.

Results Comparison

TargetMechanical APDL Ratio
Modal Frequency f (Hz)42.6542.631.00
PSD Freq (Hz)42.6642.631.00
Peak d PSD(mm2/Hz)180.90179.18 [1]0.99
Peak stress PSD(N/mm2)2 /Hz58515.6057848.39 [1]0.99

  1. The peak value occurred at frequency 42.63 Hz.