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Cyclic Jacobi Method
This program uses the Cyclic Jacobi method to solve the symmetric eigenvalue problem:
Ax= lamba * Bx
Program Notes:
The inputs to this program are as follows:
*N. the size of the problem to be solved
*The number of significant figures desired in the eigenvalues
*The elements of matrix A (only the upper triangle need be entered)
*The elements of matrix B (only the diagonal need be entered)
The maximum problem size allowed in this program is controlled by the DIM statements. To alter the problem size, modify the DIMs as follows:
DIM A(N,N), B(N), U(N,N) where N is the maximum size dimension.
The eigensolution is normalized with respect to matrices A and B as follows:
XTBx = l
and
XTAx = (lamda)
where l is the identify matrix
Example:
Compute the natural vibration frequencies and mode shapes of the shear building shown below:
The free vibration dynamic equilibrium equation can be reduced to:
KO = W2MO,
where K is the stiffness matrix
M is the mass matrix of the structure
W is the natural circular frequency
0 is the corresponding vibration mode shape
Downloads:
Basic program - liberty basic - lbcjm.bas
Basic program - qbeigcj.bas - Qbasic program
Test case:
EIGENVALUES & EIGENVECTORS
USING THE CYCLIC JACOBI METHOD
ENTER SIZE OF PROBLEM (MATRIX)
N= ? 3
NUMBER OF SIGNIFICANT FIGURES? 5
ENTER UPPER TRIANGLE
OF MATRIX A , BY COLUMNS
ENTER UPPER PART OF COLUMN 1
A(1,1) =?600
ENTER UPPER PART OF COLUMN 2
A(1,2) =?-600
A(2,2) =?1800
ENTER UPPER PART OF COLUMN 3
A(1,3) =?0
A(2,3) =?-1200
A(3,3) =?3000
ENTER ELEMENTS OF
DIAGONAL MATRIX B
B(1) = ?1
B(2) = ?1
B(3) = ?2
TOLERANCE= 1.0e-10
SOLUTION
********
NO. OF ROTATIONS REQUIRED = 7
EIGENVALUE 1 IS 237.285069
ITS EIGENVECTOR IS
0.80832648
0.48865347
0.23219182
PRESS ENTER TO CONTINUE
?
EIGENVALUE 2 IS 1042.06808
ITS EIGENVECTOR IS
-0.54179432
0.3991828
0.52302582
PRESS ENTER TO CONTINUE
?
EIGENVALUE 3 IS 2620.64685
ITS EIGENVECTOR IS
0.23036323
-0.77580338
0.41536845
PRESS ENTER TO CONTINUE
?
END OF PROGRAM
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