Normalization of Vibration

Normalization is a process that scales the dynamic responses of a structure to produce modal responses. These modal responses are useful in estimating the mode shape of a similar dynamic system when its mass and stiffness proportion is the same. One of the ways to scale the responses is mass-normalization.

The matrix of modal responses is also known as eigenvectors, while the square of natural frequency of vibration modes can also be known as eigenvalue. One most important property of eigenvector is orthogonality.

Both mass-normalization and orthogonality of eigenvectors are discussed through a 2-DOF example. 

The following shows the derivation and example of normalization and checking for orthogonality of eigenvectors. Watch the video above for full details.

Mass normalization and example

Defining eigenvector and eigenvalue - 1

Defining eigenvector and eigenvalue - 2

Defining orthogonality of eigenvector - 1

Defining orthogonality of eigenvector - 2

Check for orthogonality of eigenvector in example