TEST CASE 8.2 DYNAMIC PROBLEM UNDER ACTION OF HARMONIC DISTURBING FORCE
Reference:
T. Thomson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965, pg. 99, article 4.1.
Problem description:
A rack with a concentrated mass M at its free end is loaded with a transverse harmonic force F(t) (see a graph of the change in force intensity over time in the figure below). Determine the transverse displacement u at the moment T = 0.1 sec, T = 0.2 sec, T = 0.3 sec.
Problem sketch:
Type of created problem:
Flat frame (X, Z, UY).
Geometric characteristics:
L = 2.54 m.
Material properties:
EI_{y} = 7028.62 t·m^{2}.
Boundary conditions:
Node 1: X = Z = UY = 0;
Node 2: Z = 0.
Loads:
Concentrated mass: М = 1.785 t·sec^{ }^{2}/m;
Harmonic influence: F = 45.36·sin(θt) t;
Circular frequency: θ = 30 rad/sec.
Model description:
The system is modeled by one bar element (FE 10 type). Perform calculation of dynamics in time (integration time 0.3 sec, integration step 0.001 sec).
Analytical solution:
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
u, m; T = 0.1 sec |
0.04093 |
0.04089 |
0.106 |
u, m; T = 0.2 sec |
-0.08145 |
-0.0812 |
0.307 |
u, m; T = 0.3 sec |
0.12045 |
0.12023 |
0.180 |
Moving along X at different times