We did ring down measurement of the rubber cone used for supporting the seismic isolation stacks. The resonant frequency and Q of the spring will be used for better TF of the stack later. The measured values are f =46.7 Hz, Q = 14.67. (**mass will be added later**)
[details about the measurement will be added later]
These are the results from the data Frank gave me.
There is a problem in the result. The frequency of the ring down response can vary from 42 Hz to 47 Hz. So when I fit it I cannot really get the "best" frequency fit from the whole train of data.
From figure (1)
- At point A) The data and fit seem to be well matched.
- At B) The phase of the fit curve advances the measurement ( the fit frequency is too large)
- At C) The phase of the fit curve lags the measurement (The fit frequency is too small)
- At D) The frequency totally changes causing the fit and the measurement to be almost out of phase
*fig1: showing fit with the data. Non-linearity behavior of the spring can be seen clearly.*
There are 5 sets of measurement. I notice that the nonlinear behavior was very small in the first data set which has its initial amplitude smaller than 0.4 V
fig2 Fit from data TEK00000. The initial amplitude is less than 0.4 V.
For other data sets, where their initial amplitude exceed 0.4, it does not matter where I analyze the data, fitted frequency still varies a lot. I take the data set #4, and fit the data at high amplitude and low amplitude (when it is less than .15V). The frequency still varies. See fig3 below.
*fig3: fit from data TEK00003. Even when I use data at smaller amplitude, frequency still varies from the fit, similar to what happens in fig(1).*
The problem is, the fitted frequency from fig(2) is ~ 46 Hz, while the fitted frequency (at low amplitude) from fig(3) is ~ 43 Hz. The difference is too large. So we decided to sample the frequency by averaging the frequency over 3 adjacent cycles of the ring down data, ignoring the first few peaks. Then histogram the samples.
Most of the counts are around 46.5 Hz, which is contributed mostly from the first data set where the variance is very small. I think it is ok to pick the value from that data set
f =46.7Hz, Q = 14.67. |