VM74

VM74
Transient Response to an Impulsive Excitation

Overview

Reference: W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 99, article 4.1.
Analysis Type(s): Mode-Superposition Transient Dynamic Analysis (ANTYPE = 4)
Element Type(s): Combination Elements (COMBIN40)
Input Listing: vm74.dat

Test Case

A mass supported on a spring is subjected to an impulse force F(t) and thereafter undergoes free vibration. Determine the maximum deflection ymax of the mass for the undamped case and the deflection y at time t for two damping ratios:

  • ξ = 0.0 (undamped)

  • ξ = 0.7.

Figure 103: Impulsive Excitation Problem Sketch

Impulsive Excitation Problem Sketch

Material PropertiesLoading
m = 0.5 lb-sec2/in
k = 200 lb/in

Analysis Assumptions and Modeling Notes

The node locations are arbitrarily selected. The damping coefficient c is calculated as 2ξsqrt(km) = 0.0 and 14.0 lb-sec/in for ξ = 0.0 and ξ = 0.7 respectively. A static solution is done at the first load step. The final time of 0.105 sec allows the masses to reach their largest deflections. The integration time step (0.0025 sec) is based on 1/120 of the period to allow the step changes in acceleration to be followed reasonably well and to produce sufficient printout for the theoretical comparison. The impulse is applied over one integration time step.

Results Comparison

 TargetMechanical APDLRatio
Time = 0.08 sec

Damping ratio = 0.0

y,max in0.999570.995230.996
Time = 0.1 secy, in (for damping ratio = 0.0)0.909300.92469[1]1.017
y, in (for damping ratio = 0.7)0.341800.35167[1]1.029

  1. Based on time = 0.1 + 0.0025 sec to account for finite impulse duration of 0.0025 sec.