TEST CASE 8.1 DYNAMIC PROBLEM UNDER IMPULSE ACTION
Reference:
T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 99, article 4.1.
Problem description:
A spring with a mass m at its end (point 2) is stretched by a longitudinal force F (graph in the figure) for 0.0025 seconds. Determine the displacement w of point 2 with the damping parameter ξ = 0.00 at time T = 0.0025 sec, T = 0.08 sec, T = 0.1 sec.
Problem sketch:
Type of created problem:
Flat frame (X, Z, UY).
Geometric characteristics:
Bar: L = 1 m.
Material properties:
Spring stiffness: K = EA/L = 200 tf/m.
Boundary conditions:
Node 1: X = Z = 0;
Node 2: X = 0.
Loads:
Concentrated mass: m = 0.5 t·sec^{ }^{2}/m;
Rectangular impulse: F = 4000 tf.
Model description:
The system is modeled by one bar element (type FE 10).
Analytical solution:
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
w, mm; T = 0.0025 sec |
24.995 |
25.001 |
0.024 |
w, mm; T = 0.08 sec |
999.896 |
999.97 |
0.007 |
w, mm; T = 0.1 sec |
919.32 |
919.39 |
0.008 |
Moving in Z at different times