TEST CASE 8.3 DYNAMIC PROBLEM UNDER THE IMPACT OF ACCELEROGRAM IN THREE DIRECTIONS
Reference:
Analytical solution.
Problem description:
A rack with a concentrated mass M is exposed to accelerograms in three directions. There is no damping. Determine the displacements u_{x1}, u_{x2}, u_{x3}, u_{y1}_{, }u_{y2}_{, }u_{y3}_{, }u_{z1}_{, }u_{z2}_{, }u_{z3} at the moment T = 0.1 sec, T = 0.2 sec, Т = 0.3 sec (subscripts x, y, z denote the direction, 1, 2, 3 — time points 0.1 sec, 0.2 sec, 0.3 sec, respectively).
Problem sketch:
Type of created problem:
Spatial design (X, Y, Z, UX, UY, UZ).
Geometric characteristics:
L = 2.54 m;
A = 0.0025 m^{2};
I_{y} = 5.2083·10^{-7} m^{4};
I_{z} = 5.2083·10^{-7} m^{4}.
Material properties:
E = 3·10^{6} tf/m^{2}.
Boundary conditions:
Node 1: X = Y = Z = UX = UY = UZ = 0.
Loads:
Concentrated mass: M = 2 tf;
Laws of harmonic action change:
a_{x} = 5·sin(θt) m/sec^{2},
a_{y} = 6·sin(θt) m/sec^{2},
a_{z} = 10·sin(θt) m/sec^{2};
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 is 0.3 sec, integration step is 0.0001 sec).
Analytical solution:
Calculation results:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
u_{x1}, mm |
-15.86846 |
-15.9004 |
0.201 |
u_{x2}, mm |
-34.62871 |
-34.6264 |
0.006 |
u_{x3}, mm |
-46.73764 |
-46.7344 |
0.007 |
u_{y1}, mm |
-19.04215 |
-19.0805 |
0.201 |
u_{y2}, mm |
-41.55445 |
-41.5517 |
0.007 |
u_{y3}, mm |
-56.08517 |
-56.0813 |
0.007 |
u_{z1}, mm |
- 0.19694 |
-0.1933 |
1.845 |
u_{z2}, mm |
0.04530 |
0.0438 |
3.299 |
u_{z3}, mm |
-0.48687 |
-0.4870 |
0.029 |
Moving at Т = 0.1 sec
Moving at Т = 0.2 sec
Moving at Т = 0.3 sec