40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
 PSL Not logged in Message ID: 1134     Entry time: Sun Mar 31 03:03:28 2013     In reply to: 1131     Reply to this: 1135
 Author: tara Type: Notes Category: PMC Subject: PMC Longitudinal Testing and Modal Analysis

[see PSL:1135]

I compared results between COMSOL and analytical solution. The first longitudinal mode from both results are comparable.

Peter sent me a note from Dennis about PMC longitudinal mode calculation. Dennis mentioned about a book by Young&Roark (here), so I looked it up and see how to estimate body mode frequencies of a simple block/beam.  I tried a simple geometry, a 0.1x0.1x0.175 (m) block. According to the book, cf situation 7b, table16.1 page 771, the first longitudinal mode is

f1 = (1.57/2*pi) * sqrt ( E/ rho*L^2), ), rho is the mass density of the material (2202 kg/m^3, for SiO2), E is the Young's modulus (72 GPa), L is the length of the block ( I use L = 0.175/2 because 7b situation is a uniform bar vibrates along its longitudinal axis, with upper end fixed, lower end free. This is similar to a whole beam resonate freely on both end because its center will be fix. Thus, to use the formula for our case, we have to use half length of the beam).

The analytical solution and COMSOL give f1 ~ 16 kHz. It is very strange that, according to COMSOL simulation, when the cross sectional area of the block is changed to 0.01x0.01 m^2 instead of 0.1x0.1 m^2, the frequency of the longitudinal mode does not change that much (still close to 16kHz. However, from the analytical solution, the frequency should drop by a factor of 10 ( around 165 Hz).

I'm going to think about this a bit more, but at this point, I think my COMSOL model is not correct. Might be some kind of bdy conditions that I'm missing. ELOG V3.1.3-