VM75

VM75
Transient Response to a Step Excitation

Overview

Reference: W. T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 102, article 4.3.
Analysis Type(s): Mode-Superposition Transient Dynamic Analysis (ANTYPE = 4)
Element Type(s): Combination Elements (COMBIN40)
Input Listing: vm75.dat

Test Case

A spring-mass-damping system, initially at rest, is subjected to a step force change F acting on the mass. Determine the maximum deflection umax for the undamped case. Determine the displacement u at time t for two damping ratios:

  • ξ = 0.0 (undamped)

  • ξ = 0.5

Figure 104: Step Excitation Problem Sketch

Step 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 2ξ sqrt(km) = 0.0 and 10 lb-sec/in for ξ = 0.0 and ξ = 0.5 respectively. A static solution is done at the first load step. The maximum time of 0.205 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 initial step acceleration change to be followed reasonably well and to produce sufficient printout for the theoretical comparison. POST26 is used to get displacement versus time display.

Results Comparison

 TargetMechanical APDLRatio
Time = 0.1575 secumax, in 2.00001.99921.000
Time = 0.20 secu, in (for Damping ratio = 0.0)1.65361.67231.011
u, in (for Damping ratio = 0.5)1.15311.15441.001

Figure 105: Displacement vs. Time Display

Displacement vs. Time Display