Is My Thesis on Mechanical Vibrations Ready for Expert Review?

[deadstar33]

I just submitted my final year thesis yesterday, but I was working on it right up to the submission time because there was so much work involved so I didn't get a chance to ask anyone to scan over the document to see if it reads alright from the point of view of an impartial observer. Now that all the class is finished and in celebratory mode, I don't have a hope of convincing anyone to have a look over it. I know it's a bit of a stretch, but in the off chance that somebody reading this is an engineer or an expert in mechanical vibrations and is for some reason interested in taking a brief look at my thesis, here's the link to the pdf:

http://www.4shared.com/document/3vYwlk8A/Final_Year_Project_2011.html

Also, you might want to skip the "executive summary" at the start, it was a group project and we all had to have the executive summary at the beginning of the report. Thats the only bit that I didn't write myself. Obviously I don't expect anyone to want to read an entire thesis, but even if someone was interested in scanning over it I'd appreciate it.

Thanks! Feel free to be honest with me if it sucks.

 

[JolileChat]

I'm reading it.

 

[deadstar33]

Thanks, I was a little dodgy on the physics behind the deflection pattern of a node on the string as it vibrates at its various harmonics simultaneously (the last section of chapter 8), and I had no idea why the amplitude of the vibration was increasing slightly for each cycle (the graph in that section), so I chose to not address it rather than attempt an explanation and end up sounding silly...

 

[brewnog]

Cool. I'm an engineer, a guitarist, and did my A level physics project studying the effect various effects pedals have on harmonic responses. I'll give it a read when I get a minute.

 

[revnaknuma]

I have a BS degree in physics and am an MS student of physics now.
I play stringy instruments of traditional ottoman (turkish) music, and I can play guitar in turkish style.
I have some idea about musical acoustics. I will read your thesis.
I plan to have an MS thesis on musical acoustics.

 

[revnaknuma]

However, I can't reach the link. I will try later on.
can you copy and paste your thesis here.

 

[deadstar33]

Yeah, I just attached it there to this comment. Thanks everyone for the help

 

[AlephZero]

The good news is I didn't see anything wildly "wrong", but here are a few comments (on the project, rather than the report itself)

The rig design. You seem to be exciting the string at its mid point. That means you will only excite the odd harmonics because the even harmonics have zero displacement at the mid point. Also this is not where a guitar is usually plucked. It might be worth thinking about moving the excitation point closeer to one end. I'm not a guitarist but for pianos the striking point is often 1/7 of the length of the string, which excites all the harmonics from 1 to 6 but not the seventh, which is dissonant.

Section 8.1.1. You said the discrepancy with the theoretical model could be caused by the flexibility of your test rig, or friction of the string over the "bridge" interfering with the tension measurements.

You could do the measurements increasing the tenson in steps, and then decreasing it again. If the main problem was flexibility, you would expect the results to be the same for increasing and decreasing loads. If the main problem was friction, the results would be different becase for increasing loads the tension would be lower than measured but for decreasing loads the tension would be higher.

If the problem is friction, hitting the rig with a hammer to "unlock" the friction after each change of load is often a good fix

Fig 8.5. I guess the high frequency "wiggles" are caused by the fact that you truncated the dynamics model to 21 modes. The fact that the pattern does not repeat exactly for the 5 cycles could be caused by various things, including:

1. The frequences of the FE model are not exact multiples of each other. If you included the bending stiffness of the string considered as a beam, then the frequences should not be exact multiples, but the difference will probably be very small. This is an effect called "inharmonicity" in real strings (and too much of it affects the tone of the instrument), but it is more significant for heavy gauge and wound strings.

2. More likely, this is an artefact of the numerical time-integration method. Without going into the theory, the bottom line is that the output from any numerical time integration scheme will not reproduce the "exact" frequencies from a modal analysis. The frequency error increases as the number of timesteps in each cycle of oscillation decreases, so this affects the high frequency modes more than the low frequencies.

You could check out cause #2 by running the model with a different time step (for example, double or halve it and see what happens.