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final_proj_group11/egv.m
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function [f1,f2,f3] = egv(N,P) | |
%Function solves for the natural frequency of a the beam in problem 2 and 3 | |
%given N segments and transverse load P | |
%Initialize Constants | |
E = 70*10^9; %Pa | |
dens = 2700; %kg/m^3 | |
b = 0.1; %m | |
h = 0.01; %m | |
l = 1; %m | |
%Derived variables | |
I = (b*(h^3))/12; % m^4 | |
area = b*h; %m^2 | |
%Segments | |
segl = l/N; %m - length of segment | |
%Diagonal values | |
diagonal = ((P*2)/((N^2)*E*I)) + 6; %main diagonal | |
offDiag = (-P/((N^2)*E*I)) - 4; %off-diagonal | |
%Loop through all values of A to create values | |
A = zeros(N-1,N-1); | |
for row = 1:(N-1) | |
for column = 1:(N-1) | |
%diagonal values | |
if row == column | |
A(row,column) = diagonal; | |
end | |
%off diagonal values | |
if column == row - 1 | |
A(row,column) = offDiag; | |
end | |
if column == row + 1 | |
A(row,column) = offDiag; | |
end | |
%"off-off" diagonal values | |
if column == row - 2 | |
A(row,column) = 1; | |
end | |
if column == row + 2 | |
A(row,column) = 1; | |
end | |
end | |
end | |
%Sets corner values to one less than main diagonal values | |
A(1,1) = ( (2*P) / ((N^2)*(E*I)) ) + 5; | |
A(N-1,N-1) = ( (2*P) / ((N^2)*(E*I)) ) + 5; | |
%Built in eigenvalue MATLAB function finds eigenvalues of the matrix | |
%generated for the beam | |
egv = eig(A); | |
%Plug into function for natural frequencies to solve (for first three - | |
%more can be generated with following values of egv vector) | |
f1 = sqrt((egv(1)*E*I)/dens/area/(segl^4)); | |
f2 = sqrt((egv(2)*E*I)/dens/area/(segl^4)); | |
f3 = sqrt((egv(3)*E*I)/dens/area/(segl^4)); | |
end |