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

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

 

Top View edit

 

Mode 2 edit

Front View edit

 

Top View edit

 

Mode 3 edit

Diagonal View edit

 

Top View edit