How we can use matrixes as a variables in a loop?

Question

Elyar Ghaffarian Dallali el 3 de Dic. de 2022

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https://la.mathworks.com/matlabcentral/answers/1870322-how-we-can-use-matrixes-as-a-variables-in-a-loop

Comentada: Jan el 4 de Dic. de 2022

I have a MATLAB code calculating four types of matrixes which are time dependent.

close all

clear all

clc

% FIRST HARMONIC OF WALKING PROPERTIES

% Dynamic Load = Shape function*A1.cos(B1.t+phi) , A1=W*DLF, B1=2*pi*k*fp,

% k=1 (First Harmonic), phi=0 (First Harmonic)

phi1 = 0;

load A1.mat

%B=2*pi*k*fp

load B1.mat

% V = 0.714*fs+0.055 (Velocity of Pedestrian Loading)

load V.mat

digits(2)

format shortEng

syms G1

syms t

G1 = vpa([sin(pi.*V.*t/22.9).*A1.*cos(B1.*t)],2);

%%

% MODAL PROPERTIES OF THE BEAM:

syms x

m1 = 1735*int((sin((pi*x)/22.9))^2, 0, 22.9);

% NORMALIZED MODE SHAPE:

syms phi(x)

phi(x) = sin(pi*x/22.9)/sqrt(m1);

%NORMALIZED MODAL MASS:

m = 1735*int(phi(x)^2, 0, 22.9);

% MODAL FORCE:

digits(2)

syms f1(t)

f1(t) = G1.*phi(V.*t);

% fplot(f1(t), [0,20]);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Bridge First Vertical Modal Damping Ratio:

kisi = 0.008;

% First Modal Frequency of the Beam:

omega = 8.8*pi;

%%

% MODAL PROPERTIES:

% BODY MASS:

load mp.mat

% BODY STIFFNESS:

load kp.mat

% BODY DAMPING:

load cp.mat

for i=1:1:length(mp)

m = vpa([1, mp(i,:).*phi(V(i,:)*t); 0, mp(i,:)])

k = vpa([omega^2, 0; -kp(i,:).*phi(V(i,:)*t), kp(i,:)])

c = vpa([2*kisi*omega, 0; -cp(i,:).*phi(V(i,:)*t), cp(i,:)]);

Q = vpa([G1(i,:).*phi(V(i,:)*t); 0]);

end

It is worth noting that cp, kp, mp, A1, B1, and V are vectors defined as follows;

A1=

326.673000000000

402.442987500000

478.212975000000

553.982962500000

613.125000000000

277.018704000000

341.271653400000

405.524602800000

469.777552200000

519.930000000000

224.751024000000

276.880775400000

329.010526800000

381.140278200000

421.830000000000

201.230568000000

247.904880300000

294.579192600000

341.253504900000

377.685000000000

182.936880000000

225.368073000000

267.799266000000

310.230459000000

343.350000000000

182.936880000000

225.368073000000

267.799266000000

310.230459000000

343.350000000000

182.936880000000

225.368073000000

267.799266000000

310.230459000000

343.350000000000

167.256576000000

206.050809600000

244.845043200000

283.639276800000

313.920000000000

156.803040000000

193.172634000000

229.542228000000

265.911822000000

294.300000000000

154.189656000000

189.953090100000

225.716524200000

261.479958300000

289.395000000000

117.602280000000

144.879475500000

172.156671000000

199.433866500000

220.725000000000

B1=

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

10.4876000000000

11.5363600000000

12.5851200000000

13.6338800000000

14.6826400000000

V=

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

1.24738000000000

1.36661800000000

1.48585600000000

1.60509400000000

1.72433200000000

mp=

125

106

86

77

70

64

60

59

45

cp=

135

114.480000000000

92.8800000000000

83.1600000000000

75.6000000000000

69.1200000000000

64.8000000000000

63.7200000000000

48.6000000000000

kp =

405

343.440000000000

278.640000000000

249.480000000000

226.800000000000

207.360000000000

194.400000000000

191.160000000000

145.800000000000

As it is mentioned, in the above code, m, c, k, and Q are time dependent matrixes. In the following, I want to calculated eigen values of these time dependent matrixes for different time steps which has been mentioned in vector titled 't' defined as below:

t=

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

9.17923968638266

8.37834713138565

7.70599573579136

7.13353859649341

6.64025257317036

At the end of the day, I want to calculate the value of 'A' as an output vector of the final code associated with with all of the components of vector 't'

clear all;

close all;

m = [1.0, 0.89*sin(0.19*t); 0, 120.0];

k = [760, 0; -2.9*sin(0.19*t), 400] ;

c = [0.44, 0; -0.96*sin(0.17*t), 140 ];

mk = -m\k;

mc = -m\c;

B = [zeros(2), eye(2); mk, mc];

C = (1/(2*pi))*abs(eig(B)); % Calculating the Natural Frequency of the human_bridge system

A =C(1)

2 comentarios
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Dyuman Joshi el 4 de Dic. de 2022

Format your code properly.

Jan el 4 de Dic. de 2022

@Elyar Ghaffarian Dallali: Please clean up the question. The huge pile of blank space impedes the reading. In addition the question "use matrices as variables" is not clear.

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