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#### TEST CASE 8.4 DYNAMIC PROBLEM UNDER THE IMPACT OF SEISMOGRAMS IN THREE DIRECTIONS

Reference:

Analytical solution.

Problem description:

A rack with a concentrated mass M is exposed to seismograms in three directions at the restraint point. 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:

Ux = -3.5636·sin(θt) m/sec2,

Uy = -4.27637·sin(θt) m/sec2,

Uz = -6.9·10-4·sin(θt) m/sec2;

Circular frequency: θ = 30 rad/sec.

Model description:

The system is modeled by one rod element (FE 10 type). Perform calculation of dynamics in time (integration time 0.3 sec, integration step 0.0001 sec).

Analytical solution:

Calculation results:

 Target value Analytical solution LIRA 10 Deviation, % ux1, mm -15.86846 -15.86331 0.030 ux2, mm -34.62871 -34.61757 0.030 ux3, mm -46.73764 -46.69195 0.098 uy1, mm -19.04215 -19.03605 0.032 uy2, mm -41.55445 -41.54131 0.032 uy3, mm -56.08517 -56.03075 0.097 uz1, mm - 0.19694 -0.19735 0.206 uz2, mm 0.04530 0.04485 0.990 uz3, mm -0.48687 -0.48880 0.396

Moving at Т = 0.1 sec

Moving at Т = 0.2 sec

Moving at Т = 0.3 sec