Catching up on eigenfrequencies

Finally exam period is over and we’re back to normal studies. Well, not actually.

This last week has been quite a challenging one. I’ve focused a lot on trying to get up to speed with the other guys in AESIR (the student rocketry association) as well as learning the product and machine parts course during the exam period. This means I’ve lagged behind a bit in the sound and vibrations course, and we had a partial exam in that this week.

It just so happens that we’ve had a lot of partial exams in our courses lately, only broken up by the actual exam period for finals. So this is the 5th week in a row with some form of exam. Anyways, enough complaining.

Transmission and reflection of vibrations through a dimension change in a beam.

This week I basically threw everything else out the window and tried to focus on the sound and vibrations course. Mainly on the transmission of vibrations through solid structures. The tricky part here is that you can get reflections of waves at ends and size changes. So there can be interference between incoming and reflected waves. In beams you can also get something called the eigenfrequency (resonance), which is dependent on material parameters as well as the length and shape of the beam. So it’s back to reading up on some solid mechanics as well.

Every eigenfrequency has a eigenform of vibration. Why is this important? Well, you want to avoid building structures that will resonate in a frequency you will input into the structure (deliberate or undeliberate). A common example people talk about is the Tacoma bridge collapse, where a whole bridge collapse because the wind made it vibrate at it’s eigenfrequency.

Some eigenforms of vibration (marked with red), that can occur in a beam.

The concept of all this, as well as how material parameters and structure shape affects these resonance frequencies and reflections is something that didn’t take long to understand. However, since I’m still a bit shaky on the underlying way we use math to describe vibrations and waves, I can’t say that I fully understand this yet (there is a lot of imaginary numbers).

It’s not that the math, or the way we apply it is really that hard. It’s just that I learn best by really deepdiving into a subject and give myself time to do the mathematical proofs of the concepts as well. I find this is way more work than what is expected of me to just get a passing grade. But with a better understanding I can afford to study less during exam period, which usually means I’ll make silly mistakes on exam questions, but at least have a deeper understanding for what I’m doing.

We also just started the Thermodynamics course this week, and I haven’t really put any time or effort into that course yet. I guess that’s going to be the project of next week. But for now, it’s back to AESIR and building rocket parts during the weekend.