Experimental Procedure

As with the setup in general, many of the elements of the experimental procedure are shared among the experiments of each chapter. An example of this procedure is as follows (where the static compression mechanism is the soft linear spring configura- tion):

1. Electrical connections are made with coaxial BNC cables.

2. Connect the actuator input to the output of the voltage amplifier (as shown in figure 1.3). Connect a ‘T’ connector to one of the output channels on the DAQ board. Connect one terminal of the ‘T’ connector to an input channel on the DAQ board to directly measure the generated signal. Connect the input of the voltage amplifier to the other terminal of the ‘T’ connector, which is connected to the output channel on the DAQ board. Check the gain on the voltage amplifier.

3. If used, connect the output of the strain gage embedded in the piezoelectric actuator to the strain gage amplifier and monitor. Connect the output of the

strain gage amplifier and monitor to an input channel on the DAQ board. Turn on the strain gage amplifier and monitor.

4. Turn on the DAQ board and the voltage amplifier and set the DC offset voltage to be half of the amplifier positive voltage range. This is performed at the beginning of the procedure to allow the actuator enough time to reach a steady static offset.

5. Prepare the polycarbonate guide rods by sanding them with fine grain sand paper (and regular fine grain paper). Remove any residue with a soft clean cloth. Prepare the particles composing the granular crystal by cleaning with isopropanol.

6. Fix the actuator to the mounting block, and fix the mounting block to the optical table.

7. Align the polycarbonate alignment plates in front of the actuator, and place at regular intervals to span the length of the granular crystal. Position extra guide plates on the opposite side of the actuator mounting block to support any remainder of the polycarbonate guide rods.

8. Insert the polycarbonate guide rods through the polycarbonate guide plates and the actuator mounting block designed for 19.05 mm diameter particles. If using four rods, leave one rod off until the end so that the granular crystal particles can be positioned.

9. Position the particles composing the granular crystal onto the polycarbonate guide rods. If using any smaller radii particles, use a polycarbonate or teflon guide ring with 19.05 mm outer diameter to axially align the particle.

10. Replace desired particles with the custom in-situ piezoelectric sensors (see figure

1.4). Connect the sensor outputs to the input of voltage amplifiers (and or low-pass filters). Check the gains on the voltage amplifiers, and set the cutoff frequency of the low-pass filters to 30 kHz. Connect the output of the voltage

amplifiers to an input channel on the DAQ board. Turn on the voltage amplifiers and low-pass filters.

11. Place the soft linear spring (with outer diameter of approximately 18.5 mm) at the end of the granular crystal, opposite of the piezoelectric actuator.

12. Place the static load cell with the teflon holder behind the soft linear spring (with respect to the piezoelectric actuator). Connect the two reference voltage inputs of the static load cell to the 5 V DC source on the DAQ board. Connect the two measurement outputs of the static load cell to the voltmeter.

13. If used, insert the fourth (or third and fourth) polycarbonate guide rod.

14. Position the second steel boundary block behind the static load cell so that the linear spring and the crystal are compressed. Measure the static load applied with the static load cell (displayed on the voltmeter). Fix the steel boundary block to the optical table when the desired static load is reached.

15. In any MATLAB code used to drive the data acquisition: set the gains, the number and names of any input and output channels, and the sampling rate (as described in previous sections).

16. The signal generation and measurement (via the DAQ board) can now be con- ducted nearly simultaneously across all channels (the input channels are mul- tiplexed, such that they are sampled sequentially at the DAQ board maximum sample rate, and the signals are recorded at the user specified sampling fre- quency). The measured signals (including the feedback from the output chan- nel) can now be recorded via MATLAB and post processed as desired.

17. Acquire data without any driving signal to assure that all sensors have dis- charged and reached a steady static value (repeat this step before any data acquisition).

18. Conduct a calibration run using the signals to be used in the specific experi- ment. Make sure the gains and the DAQ input voltage ranges are set so that

the acquired signal voltages closely match the DAQ input voltage ranges. In- clude a check in the data acquistion code to make sure the voltage range is not approached and exceeded by the acquired signals.

19. To characterize the linear spectrum of the granular crystal: apply a long-time (1 to 2 seconds) low-amplitude (compared to the static load [greater than 1%]) bandwidth-limited noise signal via the piezoelectric actuator. Linearly ramp the generated signal at the beginning and end to minimize transient response. Re- peat over multiple iterations (greater than 8). In post-processing, calculate the PSD of a time-window which avoids transients caused by turning on and off the signal, for each repetition. The PSD can be normalized by the measured signal voltage (from the DAQ board output feedback channel) and averaged (in the frequency domain) over all repetitions. The spectrum can then be normalized by the average PSD level in the transmitting bands.

20. To characterize any other relevant phenomena, a similar procedure can be used as in the previous step, however the generated signal can be replaced with any other arbitrary signal (as described in each of the following chapters).