%****************************************************************************
%****************************************************************************
%********************VARIBLADEANALYSIS **********************************
%****************************************************************************
%************************* Written by ******************************************
%****************************************************************************
%******************* TARTIBU KWANDA 2008**********************************
%****************************************************************************
%****************************************************************************
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%Variable length blade finite element program. Two portions of beam: hollow beam %(fixed portion) and solid beam (moveable portion). Solves for eigenvalues and eigenvectors of %stepped beam with user defined dimensions and configurations. This program can calculate the %natural frequencies of different beam geometries and configurations ( position of moveable portion)
%default values are included in the program for the purpose of showing how to input data.
echo off
clf;
clear all;
inp = input('Input "1" to enter beam dimensions, "Enter" to use default ... ');
if (isempty(inp))
inp = 0;
else
end
if inp == 0
% input beam's geometries and material's properties
% xl(i) = length of element (step)i
% w(i) = width of element (step)i
% t(i) = thickness of element (step)i
% e = Young's modulus
% bj = global degree of freedom number corresponding to the jth local degree
% of freedom of element i
% a(i) = area of cross section of element i
% ne = number of elements
% n = total number of degree of freedom
% no = number of nodes
% wa = width of hollow for the first portion of stepped beam
% ta = thickness of hollow for the first portion of stepped beam
format long
beamconfiguration = 1;
n1 = 10;
n2 = 10;
l1 = 1000;
l2 = 1000;
h1 = 1000/10;
h2 = 1000/10;
xl = [h1*ones(1,n1) h2*ones(1,beamconfiguration-1)];
w1 = 60;
w2 = 50;
w = [w1*ones(1,n1) w2*ones(1,beamconfiguration-1)];
t1 = 20;
t2 = 10;
t = [t1*ones(1,n1) t2*ones(1,beamconfiguration-1)];
wh = 50;
th = 10;
wa = [wh*ones(1,beamconfiguration-1) 0*ones(1,n2)];
ta = [th*ones(1,beamconfiguration-1) 0*ones(1,n2)];
% configurations of stepped beam:
% beamconfiguration ? n1 & n2
% for configuration 1, w = [w1*ones(1,n1) w2*ones(1,1-1)],
% t = [t1*ones(1,n1) t2*ones(1,1-1)]
% wa = [wh*ones(1,1-1) 0*ones(1,n2)],
% ta = [th*ones(1,1-1) 0*ones(1,n2)]
% for configuration 2, w = [w1*ones(1,n1) w2*ones(1,2-1)]
% t = [t1*ones(1,n1) t2*ones(1,2-1)]
% wa = [wh*ones(1,2-1) 0*ones(1,n2)]
% ta = [th*ones(1,2-1) 0*ones(1,n2)]
% for configuration 3, w = [w1*ones(1,n1) w2*ones(1,3-1)]
% t = [t1*ones(1,n1) t2*ones(1,3-1)]
% wa = [wh*ones(1,3-1) 0*ones(1,n2)]
% ta = [th*ones(1,3-1) 0*ones(1,n2)]
% for configuration 4, w = [w1*ones(1,n1) w2*ones(1,4-1)]
% t = [t1*ones(1,n1) t2*ones(1,4-1)]
% wa = [wh*ones(1,4-1) 0*ones(1,n2)]
% ta = [th*ones(1,4-1) 0*ones(1,n2)]
% for configuration 5, w = [w1*ones(1,n1) w2*ones(1,5-1)]
% t = [t1*ones(1,n1) t2*ones(1,5-1)]
% wa = [wh*ones(1,5-1) 0*ones(1,n2)]
% ta = [th*ones(1,5-1) 0*ones(1,n2)]
xi = [40000 40000 40000 40000 40000 40000 40000 40000 40000 40000];
a = [1200 1200 1200 1200 1200 1200 1200 1200 1200 1200];
e = 206e+6;
rho = 7.85e-6;
bj = [1 2 3 4;3 4 5 6;5 6 7 8;7 8 9 10;9 10 11 12;11 12 13 14;13 14 15 16;15 16 17 18;17 18 19 20;19 20 21 22;21 22 23 24;23 24 25 26;25 26 27 28;27 28 29 30;29 30 31 32; 31 32 33 34;33 34 35 36;35 36 37 38;37 38 39 40;39 40 41 42];
ne = 20;
n = 22;
else
beamconfiguration = input ('Input beamconfiguration of stepped beam, default 1 ... ');
if (isempty(beamconfiguration))
beamconfiguration = 1;
else
end
n1 = input ('Input number of elements for the first portion of stepped beam, default 10 ... ');
if (isempty(n1))
n1 = 10;
else
end
n2 = input ('Input number of elements for the second portion of stepped beam, default 10 ... ');
if (isempty(n2))
n2 = 10;
else
end
l1 = input ('Input length of first portion of stepped beam, default 1000, ... ');
if (isempty(l1))
l1 = 1000;
else
end
l2 = input ('Input length of second portion of stepped beam, default 1000, ... ');
if (isempty(l2))
l2 = 1000;
else
end
w1 = input ('Input width of first portion of stepped beam, default 60, ... ');
if (isempty(w1))
w1 = 60;
else
end
w2 = input ('Input width of second portion of stepped beam, default 50, ... ');
if (isempty(w2))
w2 = 50;
else
end
t1 = input ('Input thickness of first portion of stepped beam, default 20 , ... ');
if (isempty(t1))
t1 = 20;
else
end
t2 = input ('Input thickness of second portion of stepped beam, default 10 , ... ');
if (isempty(t2))
t2 = 10;
else
end
wh = input ('input width of hollow of first portion of stepped beam, default 50, ... ');
if (isempty(wh))
wh = 50;
else
end
th = input ('input thickness of hollow of first portion of stepped beam, default 10, ... ');
if (isempty(th))
th = 10;
else
end
e = input('Input modulus of material, mN/mm^2, default mild steel 206e+6 ... ');
if (isempty(e))
e=206e+6;
else
end
rho = input('Input density of material,kg/mm^3 , default mild steel 7.85e-6 ... ');
if (isempty(rho))
rho = 7.85e-6;
else
end
bj = input('Input global degree of freedom, default global degree of freedom [1 2 3 4;3 4 5 6;5 6 7 8;7 8 9 10;9 10 11 12;11 12 13 14;13 14 15 16;15 16 17 18;17 18 19 20;19 20 21 22;21 22 23 24;23 24 25 26;25 26 27 28;27 28 29 30;29 30 31 32; 31 32 33 34;33 34 35 36;35 36 37 38;37 38 39 40;39 40 41 42]; ... ');
if (isempty(bj))
bj =[1 2 3 4;3 4 5 6;5 6 7 8;7 8 9 10;9 10 11 12;11 12 13 14;13 14 15 16;15 16 17 18;17 18 19 20;19 20 21 22;21 22 23 24;23 24 25 26;25 26 27 28;27 28 29 30;29 30 31 32; 31 32 33 34;33 34 35 36;35 36 37 38;37 38 39 40;39 40 41 42];
else
end
end
ne = n1+beamconfiguration-1;
h1 = l1/n1;
h2 = l2/n2;
xl = [h1*ones(1,n1) h2*ones(1,beamconfiguration-1)];
w = [w1*ones(1,n1) w2*ones(1,beamconfiguration-1)];
t = [t1*ones(1,n1) t2*ones(1,beamconfiguration-1)];
wa = [wh*ones(1,beamconfiguration-1) 0*ones(1,n2)];
ta = [th*ones(1,beamconfiguration-1) 0*ones(1,n2)];
% calculate area (a), area moment of Inertia (xi) and mass per unit of length (xmas) of
% the stepped beam
a = (w.*t)-(wa.*ta);
% define area moment of inertia according to flap-wise or edge-wise
% vibration of the stepped beam.
vibrationdirection = input('enter "1" for edge-wise vibration, "enter" for flap-wise vibration ... ');
if (isempty(vibrationdirection))
vibrationdirection = 0;
else
end
if vibrationdirection == 0
xi=((w.*t.^3)-(wa.*ta.^3))/12;
else
xi=((t.*w.^3)-(ta.*wa.^3))/12;
end
for i=1:ne
xmas(i)=a(i)*rho;
end
% Size the stiffness and mass matrices
no = ne+1;
n = 2*no;
bigm = zeros(n,n);
bigk = zeros(n,n);
% Now build up the global stiffness and consistent mass matrices, element
% by element
for ii=1:ne
ai = zeros(4,n);
i1=bj(ii,1);
i2=bj(ii,2);
i3=bj(ii,3);
i4=bj(ii,4);
ai(1,i1)=1;
ai(2,i2)=1;
ai(3,i3)=1;
ai(4,i4)=1;
xm(1,1)=156;
xm(1,2)=22*xl(ii);
xm(1,3)=54;
xm(1,4)=-13*xl(ii);
xm(2,2)=4*xl(ii)^2;
xm(2,3)=13*xl(ii);
xm(2,4)=-3*xl(ii)^2;
xm(3,3)=156;
xm(3,4)=-22*xl(ii);
xm(4,4)=4*xl(ii)^2;
xk(1,1)=12;
xk(1,2)=6*xl(ii);
xk(1,3)=-12;
xk(1,4)=6*xl(ii);
xk(2,2)=4*xl(ii)^2;
xk(2,3)=-6*xl(ii);
xk(2,4)=2*xl(ii)^2;
xk(3,3)=12;
xk(3,4)=-6*xl(ii);
xk(4,4)=4*xl(ii)^2;
for i=1:4
for j=1:4
xm(j,i)=xm(i,j);
xk(j,i)=xk(i,j);
end
end
for i=1:4
for j=1:4
xm(i,j)=(((xmas(ii)*xl(ii))/420))*xm(i,j);
xk(i,j)=((e*xi(ii))/(xl(ii)^3))*xk(i,j);
end
end
for i=1:n
for j=1:4
ait(i,j)=ai(j,i);
end
end
xka=xk*ai;
xma=xm*ai;
aka=ait*xka;
ama=ait*xma;
for i=1:n
for j=1:n
bigm(i,j)=bigm(i,j)+ama(i,j);
bigk(i,j)=bigk(i,j)+aka(i,j);
end
end
end
% Application of boundary conditions
% Rows and columns corresponding to zero displacements are deleted
bigk(1:2,:) = [];
bigk(:,1:2) = [];
bigm(1:2,:) = [];
bigm(:,1:2) = [];
% Calculation of eigenvector and eigenvalue
[L, V] = eig (bigk,bigm)
% Natural frequency
V1 = V.^(1/2)
W = diag(V1)
f=W/(2*pi)
| Attachment | Size |
|---|---|
| Doc1.doc | 29.5 KB |