User:Eml4500.f08.team.allen./hw4

Eigenvalues and Eigenvectors
Zero Eigenvalues correspond to rigid body motion and zero stored elastic energy.

$$ \mathbf{k}\mathbf{u}\mathbf{i} = \mathbf{0}\mathbf{u}\mathbf{i} $$

The linear combination of $$ \left\{\mathbf{u}_{i}, i=1,...,4 \right\}$$ The equation which defines $$ \mathbf{w} $$ is $$ \sum_{i=1}^{4}{\alpha i\mathbf{u}_{i}}=:\mathbf{w} $$

Homework
The following Matlab code was used to solve for the eigenvalues of the Global Stiffness Matrix of the two truss problem:

Where the eigenvector is given as $$\lambda = \begin{Bmatrix} 0\\ 0\\ 0\\ 0\\ 1.4706\\ 10.0294 \end{Bmatrix} $$