--matlab Program for approximate solution of natural frequency of simply supported beam by transfer matrix method

Approximate solution of natural frequency of simply supported beam by the method of% transfer matrix clcclearsyms p qSp = sym (' [1 0 0 0;0 1 0 0;0        0 1 0;x 0 0 1] '); % point transfer Matrix SF = Sym (' [1 1 1/2 1/6;0 1 1 1/2;0 0 1 1;0  0 0 1] '); % field transfer Matrix n = input (' Input partition Unit number: ');         S = ((sf*sp) ^ (n-1)) *sf; % of the transfer matrix between the two ends of the support for the natural frequency xs = solve (S () *s (3,4)-S (1,4) *s (3,2)); xs = sort (double (XS)); xt = Xs*n^4;xt = sqrt (XT); Xe (1:n-1) = (    pi* (1:n-1)). ^2; % exact Solution XE = Xe '; fprintf (' Result of transfer matrix method: \ n ') for i = 1:n-1 fprintf ('%d ' natural frequency:%8.4f (ei/ml^3) ^ (end) \ n ', i,xt (i)) end% modal step = 1/n;f    or i = 1:n-1 F0 =-S (3,2)/S (3,4);    F0 = Subs (F0, ' x ', xs (i));    XK (:, 1) = [0 1 0 F0] ';        For j = 2:n+1 XK (:, j) = Sf*sp*xk (:, j-1);    XK (:, j) = Subs (Xk (:, j), ' X ', xs (i));    End xkk = XK (1,2:n);    XKK = Xkk/max (ABS (XKK));    XKK = double (XKK);    Xkk = Real (XKK);    if (XKK (1) <0) Xkk =-XKK; End fprintf ('%d-order modal: ', i) disp (XKK) figure () plot (0:step:1,[0 Xkk 0].*abs (sin (i*pi*)), ' Ro ') hold    on xx = 0:pi/200:1;  Plot (Xx,sin (i*pi*xx), ' B ') endfprintf (' The result of the exact solution: \ n ') for i = 1:n-1  fprintf ('%d-order natural frequency:%8.4f (ei/ml^3) ^ (a ") \ n ', I,xe (i)) end 

Operation Result:

Input Partition number: 5
The result of the transfer matrix method:
1th-Order Natural frequency: 9.8684 (ei/ml^3) ^ (1/2)
2nd-Order Natural frequency: 39.3808 (ei/ml^3) ^ (1/2)
3rd-Order Natural Frequency: 87.1779 (ei/ml^3) ^ (1/2)
4th-Order Natural Frequency: 143.5557 (ei/ml^3) ^ (1/2)
1th-Order modal: 0.6180 1.0000 1.0000 0.6180

2nd-order modal: 1.0000 0.6180-0.6180-1.0000

3rd-order modal: 1.0000-0.6180-0.6180 1.0000

4th-Order modal: 0.6180-1.0000 1.0000-0.6180

The result of the exact solution:
1th-Order Natural frequency: 9.8696 (ei/ml^3) ^ (1/2)
2nd-Order Natural frequency: 39.4784 (ei/ml^3) ^ (1/2)
3rd-Order Natural Frequency: 88.8264 (ei/ml^3) ^ (1/2)
4th-Order Natural Frequency: 157.9137 (ei/ml^3) ^ (1/2)

--matlab Program for approximate solution of natural frequency of simply supported beam by transfer matrix method