 Register   #### 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 ux1, ux2, ux3, uy1, uy2, uy3, uz1, uz2, uz3 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 m2;

Iy = 5.2083·10-7 m4;

Iz = 5.2083·10-7 m4.

Material properties:

E = 3·106 tf/m2.

Boundary conditions:

Node 1: X = Y = Z = UX = UY = UZ = 0.

Concentrated mass: M = 2 tf;

Laws of harmonic action change:

ax = 5·sin(θt) m/sec2,

ay = 6·sin(θt) m/sec2,

az = 10·sin(θt) m/sec2;

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, % ux1, mm -15.86846 -15.9004 0.201 ux2, mm -34.62871 -34.6264 0.006 ux3, mm -46.73764 -46.7344 0.007 uy1, mm -19.04215 -19.0805 0.201 uy2, mm -41.55445 -41.5517 0.007 uy3, mm -56.08517 -56.0813 0.007 uz1, mm - 0.19694 -0.1933 1.845 uz2, mm 0.04530 0.0438 3.299 uz3, 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