VM53

VM53
Vibration of a String Under Tension

Overview

Reference: W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 264, article 8.2.
Analysis Type(s):
Static Analysis (ANTYPE = 0)
Mode-frequency Analysis (ANTYPE = 2)
Element Type(s): 3D Spar (or Truss) Elements (LINK180)
Input Listing: vm53.dat

Test Case

A flexible string with mass per unit length ρA is fixed at the ends and stretched to an initial strain εo. Determine the stress σ and force F in the string under these conditions. Determine the first three natural frequencies fi of lateral vibration of the stretched string.

Figure 77: String Under Tension Problem Sketch

String Under Tension Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
ρ = 0.00073 lb-sec2/in4
= 100 in
A = 0.00306796 in2
εo = 0.00543228

Analysis Assumptions and Modeling Notes

Enough elements are selected so that the same model can be used to adequately characterize the dynamic analysis. Linear perturbation modal analysis is performed to determine the frequencies of the pre-stressed structure

The Block Lanczos method for eigenvalue extraction is chosen solely for the sake of completeness in this manual. Other methods would also be suitable. Only the first three modes are requested.

Results Comparison

 TargetMechanical APDLRatio
StaticF, lb500.00499.991.000
Stress, psi162,974.162,9741.000
Modalf1 , Hz74.70874.8901.002
f2 , Hz149.42150.8751.010
f3 , Hz224.12229.0601.022