An Eigenvalue Problem — Lesson 3

An eigenvalue problem. This title sounds a bit esoteric and may be intimidating, but actually it is not. Stay with me. How do we go from our time-domain solution in the equations of motion to the frequency domain? The eigenvalue discussion will answer these questions! But first, what is the meaning of eigenvalue? It comes from the German word "eigen" which means "own, unique to, or characteristic." This actually will make sense because the values from the matrix, or eigenvalues, are unique and characteristic of that matrix. We will see in our study of dynamics that they elegantly characterize the natural frequencies of a structure.

So, nearly any structure you can think of will have natural frequencies.

An audio speaker has natural frequencies that get excited by the electromagnet behind the speaker. In this case, the effect is quite visible.

In this lesson we will explore and solve the eigenvalue problem, transforming from the time domain to the frequency domain. We will also look at the question of how many natural frequencies a structure has and whether they are all equally important.

Lecture

Alternate video link.

Handout

Here are the accompanying handout slides for this lesson.