VM81

VM81
Transient Response of a Drop Container

Overview

Reference: W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 110, ex. 4.6-1.
Analysis Type(s):
Full Transient Dynamic Analysis (ANTYPE = 4)
Mode-Superposition Transient Dynamic Analysis (ANTYPE = 4)
Element Type(s):
Combination Elements (COMBIN40)
Structural Mass Elements (MASS21)
Gap Condition (GP)
Input Listing: vm81.dat

Test Case

A mass m is packaged in a rigid box, as shown below, and dropped through a height h. Determine the velocity and displacement y of the mass at impact and the maximum displacement of the mass. Assume that the mass of the box is large compared to that of the enclosed mass m and that the box remains in contact with the floor after impact.

Figure 113: Drop Container Problem Sketch

Drop Container Problem Sketch

Material PropertiesGeometric PropertiesLoading
m = 0.5 lb-sec2/in
k = 1973.92 lb/in
h = 1 in
g = 386 in/sec2

Analysis Assumptions and Modeling Notes

The node locations are arbitrarily selected. The final time of 0.11 sec allows the mass to reach its largest deflection. The integration time step (0.11/110 = 0.001 sec) is based on 1/100 of the period (during impact), to allow the initial step acceleration change to be followed reasonably well, and to produce sufficient printout for the theoretical comparison.

The problem is solved first using the full method in a nonlinear transient dynamic analysis and then using the mode-superposition transient dynamic analysis. The COMBIN40 gap is replaced by a mass and a gap condition in the mode-superposition transient dynamic analysis. POST26, the time-history postprocessor, is used to extract results from the solution phase.

Results Comparison

At Impact
Full Transient Dynamic Target Mechanical APDL Ratio[1]
Time, sec0.071980.0721.000
y, in-1.00-1.00051.001
vel, in/sec-27.79 -27.79 1.000
At zero velocity (theoretical ymax = -1.5506 in, at time = 0.100366 sec)
Full Transient Dynamic Target[2] Mechanical APDL Ratio
t = 0.100 sec y, in-1.5505-1.55031.000
t = 0.101 sec y, in-1.5502-1.55021.000
At Impact
Mode-Superposition Transient Dynamic Target Mechanical APDL Ratio[1]
Time, sec0.071980.0721.000
y, in-1.00-0.9870.987
vel, in/sec-27.79 -27.60 0.993
At zero velocity (theoretical ymax = -1.5506 in, at time = 0.100366 sec)
Mode-Superposition Transient Dynamic Target[2] Mechanical APDL Ratio
t = 0.100 sec y, in-1.5505-1.54950.999
t = 0.101 sec y, in-1.5502-1.55031.000

  1. Mechanical APDL printout does not occur at theoretical time point given. Comparisons (ratios) of the nearest time results are made with the theoretical time point given.

  2. Comparisons are made at the two time points bracketing the theoretical time of zero velocity.