University of Florida/Eml4507/s13.team4ever.Wulterkens.R6.5

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Problem 6.5 3d Mode Shapes

On my honor, I have neither given nor received unauthorized aid in doing this assignment.

Problem Statement[edit]

Determine the first 3 mode shapes of the 3D truss system from problem 6.4

Solution[edit]

The set up of the problem was the same as problem 6.4. The eigenvalues can be seen below.

Matlab code[edit]

%Makes an alternate K and M matrix to calncel rows and columns for boundary
%conditions.
Kr = K;
Mr = M;
Kr((19:30),:) = [];
Kr(:,(19:30)) = [];
Mr((19:30),:) = [];
Mr(:,(19:30)) = [];

%Find Eigenvalue and Eigenvector
[Vec Val] = eig(Kr,Mr);
Vec1 = zeros(18,1);
Vec2 = zeros(18,1);
Vec3 = zeros(18,1);
for i = 1:18
    Vec1(i) = Vec(i,1);
    Vec2(i) = Vec(i,2);
    Vec3(i) = Vec(i,3);
end

%Insert back in the values for initial conditions.
Vec1 = [Vec1;zeros(12,1)];
Vec2 = [Vec2;zeros(12,1)];
Vec3 = [Vec3;zeros(12,1)];


%Add the Eigenvectors to the nodes
X1 = zeros(10,1);
Y1 = zeros(10,1);
Z1 = zeros(10,1);
X2 = zeros(10,1);
Y2 = zeros(10,1);
Z2 = zeros(10,1);
X3 = zeros(10,1);
Y3 = zeros(10,1);
Z3 = zeros(10,1);
X = zeros(10,1);
Y = zeros(10,1);
Z = zeros(10,1);
for i = 1:10
X1(i) = Vec1((i*3)-2,1);
Y1(i) = Vec1((i*3)-1,1);
Z1(i) = Vec1((i*3),1);
X(i) = pos(1,i);
Y(i) = pos(2,i);
Z(i) = pos(3,i);
X2(i) = Vec2((i*3)-2,1);
Y2(i) = Vec2((i*3)-1,1);
Z2(i) = Vec2((i*3),1);
X3(i) = Vec3((i*3)-2,1);
Y3(i) = Vec3((i*3)-1,1);
Z3(i) = Vec3((i*3),1);
end
X1 = X+X1;
Y1 = Y+Y1;
Z1 = Z+Z1;
X2 = X+X2;
Y2 = Y+Y2;
Z2 = Z+Z2;
X3 = X+X3;
Y3 = Y+Y3;
Z3 = Z+Z3;

Code used to plot the graphs[edit]

%plot origional shape
for i = 1:25
xc = [X(conn(1,i)),X(conn(2,i))];
yc = [Y(conn(1,i)),Y(conn(2,i))];
%zc = [Z(conn(1,i)),Z(conn(2,i))];
plot(xc,yc)
axis([-6 6 -6 6])
hold on
end

%plot mode 1
for i = 1:25
xc = [X1(conn(1,i)),X1(conn(2,i))];
yc = [Y1(conn(1,i)),Y1(conn(2,i))];
%zc = [Z1(conn(1,i)),Z1(conn(2,i))];
plot(xc,yc,'r')
hold on
end

%plot mode 2
for i = 1:25
xc = [X2(conn(1,i)),X2(conn(2,i))];
yc = [Y2(conn(1,i)),Y2(conn(2,i))];
zc = [Z2(conn(1,i)),Z2(conn(2,i))];
plot(xc,yc,'r')
hold on
end

%plot mode 3
for i = 1:25
xc = [X3(conn(1,i)),X3(conn(2,i))];
yc = [Y3(conn(1,i)),Y3(conn(2,i))];
%zc = [Z3(conn(1,i)),Z3(conn(2,i))];
plot(xc,yc,'r')
hold on
end

Gif's of mode shapes[edit]

Mode 1[edit]

Front View[edit]

Mode 1 Front

Top View[edit]

Mode 1 Top

Mode 2[edit]

Front View[edit]

Mode 2 Front

Top View[edit]

Mode 2 Top

Mode 3[edit]

Diagonal View[edit]

Mode 3 Front

Top View[edit]

Mode 3 Top