Transmitter
This manuscript is going to focus on how the transmitter bender element continues to oscillate after function generator stops feeding it.
In geotechnical laboratories, bender elements are mainly used as a couple; one is used as a transmitter and the other as a receiver. Function generator is an unavoidable element in these tests; it produces a signal that transmitter senses it and oscilloscope shows that. The transmitter bender element starts to move as it senses the electricity (regarding a delay or phase), but it does not stop when the electricity goes off. What happens is that as soon as function generator stops feeding the electricity, bender element becomes a source of producing the electricity because it does not stop immediately. As below figure shows the direction of the current changes and we must be able to see the generated signal over the oscilloscope screen.
Schematic sircuit
The max. amplitude of the generated signal is not in the order of
what is made by function generator so, what is seen over the
oscilloscope is a sine wave and a straight tale (below figure). To be
able to see the signal which is produced by bender element, vertical
axis over the oscilloscope should be scaled up; it costs the nice shape
of the sine wave be lost (next figures).
Clculated frequence in kHz: 25
The distorted shape of the main signal in this view is not suitable
to be back analysed to achive parameters as its frequency. The reason is
non symmetrical deformation in its view, specially as the main cycle
approaches to its end. Vertical lines in the previous and the next few
figures are matched with:
> Start point of the signal
> End of the signal= 4*(tpeak - tstart)
Even the curvature of the main signal shows strange changes at its last branch from trough toward zero (next figures). This can be a separate topic to find out what are the causes. In master thesis by Javier Fernando Camacho Tauta (2010), he noticed there are some differences in shape between the generated signal by function generator and the actual current variation in the coils of resonant column device. He believes that it could be due to electro-mechanical inertia of the oscillator (p. 142).
Back to the main topic, persistence in the vibration of the transmitter is the result of its momentum. In spite of the function generator that can produce an exact unique cycle, bender element shows a decaying vibration after the strong initial cycle. This reality is shown in the above figure.
Does changing the scale has effect on the values, as in the amplifier, or the influence is just on appearance?
At arbitrary frequency of 19 kHz two measurements are performed; in one of them vertical scale of 20mV is used and in the other 10mV. Plotting the results on one graph shows just the scale is changed and amplification is not occurred (focus on free vibration part at the right hand side of the figure):
data set No. 2
The pattern of the wave at the right hand side of the next figure differs from its left hand side; it clearly shows oscilloscope receives the signal from the transmitter after the main signal from function generator stops.
Clculated frequence in kHz: 50
Data sets:
Hear after the laboratory measurements on various bender elements
which vibrate in air is going to be presented. The goal is to show how
amplitude of free vibration varies with frequency.
4 set of the tests are performed, just using a transmitter, an
oscilloscope and a function generator (as in the above scheme). Applied
voltage is set to 20V and sine pulses with different frequencies are
applied. Range of the applied frequencies was 1~50 kHz. Max. amplitude
of the signal in free vibration part is detected. In some cases, maybe
when excitation frequency is close to the natural frequency of the
bender element, non stability is detected in the received signal; in
these cases by zooming out on the vertical axis, the problem was solved.
Frequencies of 16 and 32 kHz in the first data set and 17kHz in the
second data set can be named. At excitation frequency equal to 8kHz in
the third set of the tests the phenomenon is seen as well (Next figure).
It is important because the successive analysis show 8kHz has been close
to the natural frequency of the bender so, detection of the frequencies
that anomalies appear on the oscilloscope has priorities.
One major cycle after function generator signal had vanished. Vertical axis divisions 50mV, dat set No.3
These are the max. amplitude in free vibration part, versus applied frequency in 4 separate set of the tests. These are performed on three different bender elements; first and the second set sounds to be performed on the same bender.
Discussion:
- Grapphs are not matched exactly because different benderes have been tested. Probably for the first and the second data set the same bender is used.
- Repeting the test with the same frequency have caused various results (vertically aligned dots); in some cases the repeated tests show close results but not in the all cases so, measurements are not always robust.
The max. measured amplitude in the first data set is almost three times higher than the same in data set No.2, while these are(?) on the same bender. In both the tests frequency step has choosen to be 2kHz; in data set No.1 even frequencies are applied and in data set No.2 odd values so, as applied frequencies differ at least 1kHz, it is logic that they show different amplitudes. From resonant graphs we know that variation of the amplitudes in vicinity of the natural frequency is huge. Furthermore it is probable that none of them approached enough to the natural frequency of the bender.
This will be verified/examined by repeating the test.- Magnitudes are generally very low (suppose 0.01 Volt). It is just 0.01/10=0.1% of the input signal! In the absence of the amplifier, it is not a high quality data although compared to the signals which are measured by seperate BE receiver, it is strong and less contaminated with reflections etc.
- Comparing data set No.3 with the previous ones, we may conclude that benders with different natural frequencies are paired in a laboratory apparatus; Although by using the amplifier the problem is solved but it is possible to improve the tests by using benders with similar natural frequencies in the same aparatus.
Furthermore it shows priority of approaches that relay on using a single bender, compared to a couple of them.
Fourier analysis:
According to the above figures natural frequencies of the transmitters can be concluded because we expect the maximum voltages be coincide with max displacements of the bender, which when bender is at the air, it occurs when the excitation frequency is close to bender´s natural frequency. Does it means that in Fourier analysis the majority would be these natural frequencies?
Free vibration part of the signals is detached to perform Fourier
analysis.
Detection of exact time in which free vibration starts is not easy
because of the distortion of the main signal when vertical axis is
zoomed over the oscilloscope (described above). As a result, part of the
main signal is considered in fft analysis, as is shown in next figure.
It can have influences over the fft analysis.
A suggestion to totally eliminate what is produced by function
generator is to couple the measurements and subtract; keeping the scale
factor over the oscilloscope the same, we can do a measurement with
bender element while another measurement with removing the connection to
the bender. Subtracting these two, the remain would be what is generated
by bender alone. As below figure shows, the amplitude of the noises is
almost the same as the amplitude of the free vibration part of the
signal; the difference is some low frequency component in the case that
bender exist. Subtraction may refine this oscillation or totally remove
that or even magnify its amplitude. It seems that although the procedure
may lead to time interval of pure free vibration of the bender but it
may change the signal over this time window.
These are the results of the fft analysis on tail of the signals.
Although low frequencies has majority but the resonant frequencies are
not detectable in all data sets.
For each frequency spectra a histogram is plotted as well. It is not a
simple histogram that just counts the number of monitored frequencies
because in that case all the histograms become similar. In the plotted
histograms the amplitudes in each bin are summed (without multiplying in
the frequency value).
Discusion:
- Although in the first two set of the tests the concluded resonant frequencies from max amplitude and fft analysis do not match but in the other tests the conclusions approve each other.
- Natural frequency of benders differ although they have more or less the same geometry. In cases that a pair of benders is used in a test, using the ones with close natural frequencies can improve the results. It can improve the quality of our products, if we are producing benders for other labs.
- In the references there is a recomendation reffering to parallel or serial wiring. (Although I can not figure out how do they may differ from theoretical point of view but) maybe we must consider the effect of wiring as well.
Differences of behaviour of various benders:
All the benders show such vibration after the main signal although
the shape of the signal and its strength varies. Different behavior of
the benders worth to be considered; beside the resonant frequency of
them which differs, as is shown above, just one of the benders showed a
neat and strong behaviour as is shown in the next figure:
Calculated frequence in kHz: 9
For a range of frequencies this bender showed a good performance
while in the others the free vibration dies very quickly. The amplitude
of the detected wave for this bender is almost 10 times higher than the
others.
As frequency increases, other vibration modes appear as well. Their
appearance can be concluded as the pattern of the waves goes away from
the free vibration of a SDOF system; the first loops in the below figure
show there are superposition of several waves. As time passes, the
higher modes damp more quickly so in the far right side of the same
figure, cycles approach to SDOF response.
Conclusion:
As the consequence of connecting the bender element, changes occurs in the free vibration part of the signal which is generated by function generator; these changes has small amplitudes compared to the generated signal. Depending on the applied frequency, the amplitude order of magnitude is 5~20 mV or even less, while the main signal is 20V. This shows the low efficiency of the benders but as this vibrations always exist and show a pattern, we may find a way to use them. At the moment there is no way to use amplifier to scale them up; the only way to monitoring them is by scaling the vertical axis on the oscilloscope and performing the test close to the natural frequency of the bender.
Code: Transmitter-06-02-2023.Rmd↩︎