ESCUELA POLITCNICA DEL EJRCITO POLICARBONATOS

ESCUELA POLITCNICA DEL EJRCITO ELEMENTOS FINITOS

CDIGO DEL PROGRAMAclear clc % Defina los parmetrosE = 7e10densidad = 2700F = inline('exp(-x/10)');L = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]q = length (L)a1= 2* quad(F,0,1)a2= 2* quad(F,1,2)a3= 2* quad(F,2,3)a4= 2* quad(F,3,4)a5= 2* quad(F,4,5)a6= 2* quad(F,5,6)a7= 2* quad(F,6,7)a8= 2* quad(F,7,8)a9= 2* quad(F,8,9)a10= 2* quad(F,9,10)A = pi* [a1, a2, a3, a4, a5, a6, a7, a8, a9, a10].^2;rho = densidad*ones (size (L));k = A*E./L;m = rho.*A.*L% Crear la matriz de rigidezV = zeros (1, q);V (q) = k (q);for n=1: q-1 for p= n: n+1 V(n) = V(n)+k (p); endendK = banded (V,-k, q)%% Crear la matriz de masaW = zeros (1, q);W (1)= 2*m (1)+2*m (2);W (q)=2*m (q);for n=2: q-1 for p= n: n+1 W(n) = W(n)+2*m (p); endendM = banded (W, m, q);M = M/6% Calcular los autovaloresB = inv (M)*K;[U, D]= eig (B)% Calcular las frecuenciasomega = sqrt (diag(D))

RESULTADOS DEL PROGRAMA

E =

7.0000e+010

densidad =

2700

L =

1 1 1 1 1 1 1 1 1 1

q =

10

a1 =

1.9033

a2 =

1.7221

a3 =

1.5583

a4 =

1.4100

a5 =

1.2758

a6 =

1.1544

a7 =

1.0445

a8 =

0.9451

a9 =

0.8552

a10 =

0.7738

m =

1.0e+004 *

3.0726 2.5156 2.0596 1.6863 1.3806 1.1303 0.9254 0.7577 0.6203 0.5079

R =

1.0e+012 *

1.4488 -0.6522 0 0 0 0 0 0 0 0 -0.6522 1.1862 -0.5340 0 0 0 0 0 0 0 0 -0.5340 0.9712 -0.4372 0 0 0 0 0 0 0 0 -0.4372 0.7951 -0.3579 0 0 0 0 0 0 0 0 -0.3579 0.6510 -0.2931 0 0 0 0 0 0 0 0 -0.2931 0.5330 -0.2399 0 0 0 0 0 0 0 0 -0.2399 0.4364 -0.1964 0 0 0 0 0 0 0 0 -0.1964 0.3573 -0.1608 0 0 0 0 0 0 0 0 -0.1608 0.2925 -0.1317 0 0 0 0 0 0 0 0 -0.1317 0.1317

K =

1.0e+012 *

1.4488 -0.6522 0 0 0 0 0 0 0 0 -0.6522 1.1862 -0.5340 0 0 0 0 0 0 0 0 -0.5340 0.9712 -0.4372 0 0 0 0 0 0 0 0 -0.4372 0.7951 -0.3579 0 0 0 0 0 0 0 0 -0.3579 0.6510 -0.2931 0 0 0 0 0 0 0 0 -0.2931 0.5330 -0.2399 0 0 0 0 0 0 0 0 -0.2399 0.4364 -0.1964 0 0 0 0 0 0 0 0 -0.1964 0.3573 -0.1608 0 0 0 0 0 0 0 0 -0.1608 0.2925 -0.1317 0 0 0 0 0 0 0 0 -0.1317 0.1317

R =

1.0e+005 *

1.1176 0.2516 0 0 0 0 0 0 0 0 0.2516 0.9151 0.2060 0 0 0 0 0 0 0 0 0.2060 0.7492 0.1686 0 0 0 0 0 0 0 0 0.1686 0.6134 0.1381 0 0 0 0 0 0 0 0 0.1381 0.5022 0.1130 0 0 0 0 0 0 0 0 0.1130 0.4112 0.0925 0 0 0 0 0 0 0 0 0.0925 0.3366 0.0758 0 0 0 0 0 0 0 0 0.0758 0.2756 0.0620 0 0 0 0 0 0 0 0 0.0620 0.2256 0.0508 0 0 0 0 0 0 0 0 0.0508 0.1016

M =

1.0e+004 *

1.8627 0.4193 0 0 0 0 0 0 0 0 0.4193 1.5251 0.3433 0 0 0 0 0 0 0 0 0.3433 1.2486 0.2810 0 0 0 0 0 0 0 0 0.2810 1.0223 0.2301 0 0 0 0 0 0 0 0 0.2301 0.8370 0.1884 0 0 0 0 0 0 0 0 0.1884 0.6853 0.1542 0 0 0 0 0 0 0 0 0.1542 0.5610 0.1263 0 0 0 0 0 0 0 0 0.1263 0.4593 0.1034 0 0 0 0 0 0 0 0 0.1034 0.3761 0.0846 0 0 0 0 0 0 0 0 0.0846 0.1693

U =

0.0424 -0.1117 -0.1746 -0.2204 0.2445 -0.2445 -0.2204 -0.1746 0.1117 0.0424 -0.0917 0.2179 0.2702 0.2190 -0.0837 -0.0837 -0.2190 -0.2702 0.2179 0.0917 0.1469 -0.2886 -0.2049 0.0516 -0.2700 0.2700 0.0516 -0.2049 0.2886 0.1469 -0.2060 0.2968 -0.0129 -0.3188 0.1947 0.1947 0.3188 0.0129 0.2968 0.2060 0.2667 -0.2264 0.2702 0.2537 0.2631 -0.2631 0.2537 0.2702 0.2264 0.2667 -0.3258 0.0790 -0.4025 0.1373 -0.3278 -0.3278 -0.1373 0.4025 0.0790 0.3258 0.3797 0.1223 0.2928 -0.4462 -0.2091 0.2091 -0.4462 0.2928 -0.1223 0.3797 -0.4242 -0.3351 0.0383 0.2757 0.4720 0.4720 -0.2757 -0.0383 -0.3351 0.4242 0.4547 0.5042 -0.4170 0.2711 0.0938 -0.0938 0.2711 -0.4170 -0.5042 0.4547 -0.4665 -0.5742 0.5986 -0.6061 -0.6086 -0.6086 0.6061 -0.5986 -0.5742 0.4665

D =

1.0e+008 *

2.9961 0 0 0 0 0 0 0 0 0 0 2.6039 0 0 0 0 0 0 0 0 0 0 2.0251 0 0 0 0 0 0 0 0 0 0 1.4499 0 0 0 0 0 0 0 0 0 0 0.9726 0 0 0 0 0 0 0 0 0 0 0.6108 0 0 0 0 0 0 0 0 0 0 0.3513 0 0 0 0 0 0 0 0 0 0 0.1750 0 0 0 0 0 0 0 0 0 0 0.0659 0 0 0 0 0 0 0 0 0 0 0.0132

omega = 1.0e+004 *

1.7309 1.6137 1.4231 1.2041 0.9862 0.7816 0.5927 0.4183 0.2567 0.1150BLADIMIR PILATASIGPgina 1