VM61

VM61
Longitudinal Vibration of a Free-free Rod

Overview

Reference:	W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 269, ex. 8.3-1.
Analysis Type(s):	Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):	3D 2 Node Beam (BEAM188)
Input Listing:	vm61.dat

Determine the first three natural frequencies f_i of a free-free rod (a rod with both ends free) having a length .

Figure 85: Rod Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

ρ = 0.00073 lb-sec²/in⁴

= 800 in

An arbitrary value of 1 is assigned to beam moment of inertia, area, and thickness. Modal analysis is performed using Block-Lanczos eigensolver.