< University of Florida < Eml4507
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
Determine the first 3 mode shapes of the 3D truss system from problem 6.4
Solution
The set up of the problem was the same as problem 6.4. The eigenvalues can be seen below.
Matlab code
%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
%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
Mode 1
Front View
Top View
Mode 2
Front View
Top View
Mode 3
Diagonal View
Top View
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