Happy World Eigenvalue Day! An annual tradition still celebrated in certain circles, albeit the radius contracting with each passing year. It was just a dream some of us had, Joni Mitchell once sang, a sentiment that applies to much more than eigenvalues in Year of our Lord 2026 but I digress.
If you'd like the full WED story, here's the original skinny; a site seemingly cursed with more popups and fewer working links each time I visit. (Someday I'll move the page to LabKitty actual, assuming that wouldn't screw the SEO pooches.)
But Eigenvalue Day it remains and the Nerd Code obliges me to regale you with an eigenvalue-themed post. So here it is.
Read on.
This year's burnt offering is a fun little browlf included with Matlab to demonstrate vibration modes (of a truss). LabKitty ported this to Javascript because LabKitty loves you.
The mode shapes are the eigenvectors of the structure stiffness matrix (assuming unit node mass) and the frequency of vibration (i.e., one over the time it takes to complete a cycle) is the associated eigenvalue (the animation here ignores the frequency scaling for simplicity).
It turns out any dynamic response of a structure (e.g., to an arbitrary loading) can be represented as a weighted sum of its modes. Usually only the first couple of modes are important, which can save much number crunching for real-world structures that contain elevently million parts.
Also, if your expected loading is close to one of the structure eigenvalues, that is called a resonance and it is a Bad Thing and you need to alter the design so the load don't do that. The classic example is the Tacoma Narrows Bridge. A less well-known example are the "pogo" oscillations that dogged the Saturn V (the glitch Apollo 13 experienced before the big ka-boom was a pogo event). There is a nice summary at vibrationdata.
Pick a mode from the pulldown menu, click start, and be amazed.
Eigenvalues!
If you'd like the full WED story, here's the original skinny; a site seemingly cursed with more popups and fewer working links each time I visit. (Someday I'll move the page to LabKitty actual, assuming that wouldn't screw the SEO pooches.)
But Eigenvalue Day it remains and the Nerd Code obliges me to regale you with an eigenvalue-themed post. So here it is.
Read on.
This year's burnt offering is a fun little browlf included with Matlab to demonstrate vibration modes (of a truss). LabKitty ported this to Javascript because LabKitty loves you.
The mode shapes are the eigenvectors of the structure stiffness matrix (assuming unit node mass) and the frequency of vibration (i.e., one over the time it takes to complete a cycle) is the associated eigenvalue (the animation here ignores the frequency scaling for simplicity).
It turns out any dynamic response of a structure (e.g., to an arbitrary loading) can be represented as a weighted sum of its modes. Usually only the first couple of modes are important, which can save much number crunching for real-world structures that contain elevently million parts.
Also, if your expected loading is close to one of the structure eigenvalues, that is called a resonance and it is a Bad Thing and you need to alter the design so the load don't do that. The classic example is the Tacoma Narrows Bridge. A less well-known example are the "pogo" oscillations that dogged the Saturn V (the glitch Apollo 13 experienced before the big ka-boom was a pogo event). There is a nice summary at vibrationdata.
Pick a mode from the pulldown menu, click start, and be amazed.
Eigenvalues!
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