VM65

VM65
Transient Response of a Ball Impacting a Flexible Surface

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): Nonlinear Transient Dynamic Analysis (ANTYPE = 4)
Element Type(s):
Structural Mass Elements (MASS21)
2D/3D Node-to-Surface Contact Elements (CONTA175)
Input Listing: vm65.dat

Test Case

A rigid ball of mass m is dropped through a height h onto a flexible surface of stiffness k. Determine the velocity, kinetic energy, and displacement y of the ball at impact and the maximum displacement of the ball.

Figure 89: Ball Problem Sketch

Ball 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 seconds 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. At release h, the mass acceleration is 386 in/sec2. Therefore, a load step with a small time period is used to ramp to the appropriate acceleration while maintaining essentially zero velocity. Displacements and velocities are listed against time in POST26 and stored kinetic energy is obtained in POST1.

The model is solved using the node-to-surface CONTA175 element.

Results

 TargetMechanical APDLRatio
CONTA175 At Impact[1]time,sec0.071980.0721.000
y displacement, in-1.0000-0.99910.999
y velocity, in/sec-27.79-27.760.999
K enrg, lb-in193.00000192.646040.998
At "Zero" Velocity[2]time,sec0.100370.101001.006
max. y displacement, in-1.5506-1.55031.000

  1. Target results are for t = 0.07198 sec. Mechanical APDL results are reported for closest time point, t = 0.072 sec.

  2. Ansys results are from the time point closest (reported in POST26) to the change in velocity from negative to positive.

Figure 90: Kinetic Energy, Velocity and Displacement vs. Time Display

Kinetic Energy, Velocity and Displacement vs. Time Display