Tools | Participation Matrix

Calculates and displays the shape Participation Matrix.

The Participation Matrix equates the shapes in one Shape Table with the shapes of another Shape Table.

Two sets of complex valued shapes can be assembled into two matrices [U] & [V], where each column of each matrix contains a shape. The two shape matrices are equated to each other with the following matrix equation,

Least-Squared-Error Solution

The Participation Matrix is computed as a least-squared-error solution to the above equation using the formula below.

The two shape matrices [U] & [V] must have some matching DOFs (shape components)
If the shapes [U] are linearly independent of one another for the matching DOFs, the Participation Matrix can be computed
Only mode shapes
are used to calculate the Participation Matrix. Modal Frequency & Damping are not used.