VM91

VM91
Large Rotation of a Swinging Pendulum

Overview

Reference: W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 138, ex. 5.4-1.
Analysis Type(s): Full Transient Dynamic Analysis (ANTYPE = 4)
Element Type(s):
3D Spar (or Truss) Elements (LINK180)
Structural Mass Element (MASS21)
Input Listing: vm91.dat

Test Case

A pendulum consists of a mass m supported by a rod of length and cross-sectional area A. Determine the motion of the pendulum in terms of the displacement of the mass from its initial position Θo in the x and y directions, δx and δy, respectively. The pendulum starts with zero initial velocity.

Figure 129: Pendulum Swing Problem Sketch

Pendulum Swing Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
m = 0.5 lb-sec2/in
= 100 in
Θo = 53.135
A = 0.1 in2
g = 386 in/sec2

Analysis Assumptions and Modeling Notes

A large deflection solution is required. An initial time step is defined over a small time increment (.01/5 = .002 sec) to allow an initial step change in acceleration to be attained. Subsequent integration time steps (1.64142/8 = .205 sec) are based on 1/24 of the period to allow the initial step change in acceleration to be followed reasonably well.

Several load steps are defined for clearer comparison with theoretical results. POST26 is used to process results from the solution phase.

Results Comparison

TargetMechanical APDLRatio
Deflectionx, in(t=period/4)-60.000-59.37380.990
Deflectiony, in(t=period/4)-20.000-20.00401.000
Deflectionx, in(t=period/2)-120.00-119.91060.999
Deflectiony, in(t=period/2)0.0000-0.06620.000
Deflectionx, in(t=3period/4)-60.000-61.88341.031
Deflectiony, in(t=3period/4)-20.000-19.98970.999
Deflectionx, in(t=period)0.0000-0.23020.000
Deflectiony, in(t=period)0.0000-0.18240.000

Figure 130: Pendulum Swing

Pendulum Swing