VM50

VM50
Fundamental Frequency of a Simply Supported Beam

Overview

Reference:	W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 18, ex. 1.5-1
Analysis Type(s):	Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):	3D 3-Node Beam (BEAM189)
Input Listing:	vm50.dat

Determine the fundamental frequency f of a simply-supported beam of length and uniform cross-section as shown below.

Figure 67: Simply Supported Beam Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

w = 1.124 lb/in

ρ = w/Ag = .000728 lb-sec²/in⁴

= 80 in

A = 4 in²

h = 2 in

I = 1.3333 in⁴

g = 386 in/sec²

This beam is modeled with arbitrary cross sections. The problem is solved using Lanczos eigensolver.

	Target	Mechanical APDL	Ratio
f, Hz	28.766	28.761	1.000