How to estimate transfer function given a transmissibility plot?

[annas425]

How would I estimate the transfer function for transmissibility given this plot:

I am told that the data does not include phase information, but assume that the phase is 0 deg at low frequency and -180 deg at high frequency. I must provide a brief rationale for each component of the transfer function. Ignore the measurement noise at frequencies larger than 10 Hz. Keep in mind the frequency units; transmissibility in dB is given on the rightside y-axis.

Thank you so much in advance! I really am struggling with this.

All I know is that {transfer function} = {output} / {input}. I do not know how to get a transfer function, just given a transmissibility vs. frequency graph.

 

[donpacino]

so from low freq to 10 hz it looks like a low pass filter. there will be a pole at 0.5 hz. the pole will have a damping ratio higher than 1 due to the large Q you see there. There are ways to calculate what the damping ratio is due to how high that peak gets.
you also nee to incorporate the bump at 3.5 Hz. I'll let you try to figure that out

give me your attempt

 

[AlephZero]

Review your notes or textbook on Bode plots. The basic idea is to approximate the plotted data by straight line segments, and then write down the transfer function that corresponds to the approximation. See www.ece.utah.edu/~ee3110/bodeplot.pdf.

 

[rude man]

I would assume real poles and zeros (no complex-conjugate poles) using Bode plots as the basis for determining the transfer function.

 

[rezeew]

To estimate the transfer function from a transmissibility plot, there are a few steps that can be followed:

1. Convert the transmissibility values from dB to a linear scale. This can be done using the formula: T = 10^(TdB/20), where T is the transmissibility in linear scale and TdB is the transmissibility in dB.

2. Plot the converted transmissibility values against the frequency. This will give a curve that represents the transfer function.

3. Determine the low frequency and high frequency limits of the plot. These will correspond to the frequencies at which the phase is 0 degrees and -180 degrees, respectively.

4. Use the low and high frequency limits to determine the amplitude and phase of the transfer function at these frequencies. The amplitude can be calculated by taking the inverse of the transmissibility value at the low frequency limit, while the phase can be calculated by subtracting 180 degrees from the phase at the high frequency limit.

5. Use the amplitude and phase values at these limits to construct the transfer function. The amplitude should decrease with increasing frequency, while the phase should change from 0 degrees to -180 degrees.

6. Finally, consider the frequency units and any measurement noise at frequencies above 10 Hz to refine the transfer function. This may involve adjusting the amplitude and phase values at the low and high frequency limits, as well as smoothing out any noise in the curve.

Overall, the rationale for each component of the transfer function is as follows:

- Amplitude: This represents the ratio of the output amplitude to the input amplitude at a given frequency. It is affected by factors such as damping and resonance in the system.

- Phase: This represents the time delay between the input and output signals at a given frequency. It is affected by the system's natural frequency and any external forces acting on the system.

- Frequency: This is the independent variable in the transfer function and represents the range of frequencies at which the system is being evaluated.

- Measurement noise: This should be ignored at frequencies above 10 Hz, as it can distort the transfer function curve and lead to inaccurate estimates.