User:EML4507.s13.team4ever.Bonner/Bonnerreport6p2

Problem R6.2
On my honor, I have neither given nor recieved unauthorized aid in doing this assignment.

Description
We are to resolve problem 4.4/5.4 but by using the method of transforming the generalized eigenvalue problem into a standard eigenvalue problem and then proceeding in the calculations.

Solution
This problem is accomplished by using the following simple transformation:

$$ K^{*} = M^{-1/2} * K * M^{-1/2} $$

The problem is carried out exactly the same as from report 5 until right before the eigenvectors are found. Instead, the eigenvalues and eigenvectors are found from the $$ K^{*} $$ matrix. Once this is done, the true eigenvalues for our system are found according to:

$$ x = M^{-1/2} * x^{*} $$

The code to solve this problem are presented below.

References for Matlab code: Team 3 Report 4 Team 7 Report 4 Team 4 Report 5

The resulting displacements were:

X1 =

0  -0.2705    0.4767   -0.6077    0.6621   -0.6638    0.5912         0   -0.1427    0.3262   -0.4835    0.5702   -0.5548    0.4132

Y1 =

0.0217  -0.0687    0.0978   -0.1125    0.1091   -0.1148   -0.2720         0    0.0032    0.0412   -0.0785    0.1042   -0.1062    0.3054

X2 =

0  -0.3958    0.4536   -0.1539   -0.3379    0.7810   -0.8311         0   -0.3426    0.6375   -0.6625    0.3889    0.0108   -0.2698

Y2 =

0.0623  -0.1362    0.1170   -0.0295   -0.0724    0.1912    0.5228         0   -0.0024    0.1013   -0.1388    0.0939   -0.0144   -0.4913

X3 =

0   0.2496   -0.5547    0.6761   -0.4979    0.1250   -0.1723         0   -0.3624    0.4730   -0.3895    0.3085   -0.3383    0.4022

Y3 =

0.0936  -0.0157   -0.0466    0.0581   -0.0157   -0.1955   -1.0802         0   -0.0593    0.0534    0.0069   -0.0549    0.1049    0.7836