Analysing the 6mm LS Mode

The LS mode can be analysed in 4 ways. The first is the traditional analysis with the mouse where the user is required to specify three points in the resonance spectrum to be used in the analysis. The second requires the user to specify the position of the resonance peak. PRAP will then determine material properties for the minimum norm. The third automatically locates the resonance peak within a specified range of frequency and then analyses for the minimum norm. The fourth uses non-linear regression to directly fit material properties to the measured resonance spectrum.

As an example, the following is a description of analysing the thickness extensional resonance of the file LS.PZF included with the PRAP demonstration. For all types of analysis;

Select the Open command from the File menu
Within the Open File dialogue box, go to the Samples sub directory and load LS.PZF. Note that this is a generated spectrum.
Ensure Thickness Extensional is selected from the Analysis menu.
From the Window menu, select whether individual data points are plotted (indicated by open red circles), and whether data points are joined (by black solid lines). Also select whether the real part of the graph should be displayed in a linear or logarithmic scale.
Select the (Rw, Xw) representation from the Transform menu.

To Analyse with the Mouse

Select what is to be determined in the analysis. Select the Analysis Settings command from the Analysis menu. Select the Options tab. Using the available check boxes, select one or more of the following options;
- Determine material constants
- Determine complex circuit constants
- Determine Van Dyke's circuit constants
- Automatically locate peak
- Points to average
The automatic peak location option will select the nearest maximum to the point clicked in the spectra when selecting the peak to be analysed. Ensure that 'Determine Parameters for Minimum Norm' is not checked.
Holding down the Ctrl key, click on the resonance peak to be analysed with the left mouse button. This must be in the top part of the spectrum graph.
The Set Resonance Order dialogue box will appear. Specify the order of the peak selected. The fundamental peak is of order 1, etc. Select OK.
Holding down the Ctrl key, click on the lower side band position with the left mouse button. This should be near the maximum in the (G/w, B/w) representation (f_s).
Holding down the Ctrl key, click on the upper side band position with the left mouse button. This should be near the minimum in the plot of Xw.

To Analyse using Minimization of the Norm

Select what is to be determined in the analysis. Select the Analysis Settings command from the Analysis menu. Select the Options tab. Using the available check boxes, select one or more of the following options;
- Determine material constants
- Determine complex circuit constants
- Determine Van Dyke's circuit constants
- Locate Nearest Peak
- Determine Parameters for Minimum Norm
- Points to average
The automatic peak location option will select the nearest maximum to the point clicked in the spectra when selecting the peak to be analysed. Ensure that 'Determine Parameters for Minimum Norm' is checked.
Holding down the Ctrl key, click on the resonance peak to be analysed with the left mouse button. This must be in the top part of the spectrum graph.
The Set Resonance Order dialogue box will appear. Specify the order of the peak selected. The fundamental peak is of order 1, etc. Select OK.

To Analyse Automatically

Select what is to be determined in the analysis. Select the Analysis Settings command from the Analysis menu. Select the Options tab. Using the available check boxes, select one or more of the following options;
- Determine material constants
- Determine complex circuit constants
- Determine Van Dyke's circuit constants
- Locate Nearest Peak
- Determine Parameters for Minimum Norm
- Points to average
The automatic peak location option will select the nearest maximum to the point clicked in the spectra when selecting the peak to be analysed. Ensure that 'Determine Parameters for Minimum Norm' is checked.
While still viewing the Analysis Settings dialogue box, select the Auto-Analysis tab. Specify the resonance peak order and the range of frequency within which the peak should be located.
Select the Auto-Analyse command from the Analysis menu.

To Analyse using Non-Linear Regression

Select what is to be determined in the analysis. Select the Analysis Settings command from the Analysis menu. Select the Options tab. Using the available check boxes, select one or more of the following options;
- Determine material constants
- Determine complex circuit constants
- Determine Van Dyke's circuit constants
- Locate Nearest Peak
- Determine Parameters for Minimum Norm
- Points to average
The last three options have no effect when performing non-linear regression.
While still viewing the Analysis Settings dialogue box, select the Regression tab. Ensure that chi squared is set as desired, and whether restraints will be used on the fitted properties. If using restraints, ensure that the range of valid material properties is as desired.
Select the Non-linear Regression command from the Analysis menu. This invokes the Initial Parameter Values dialogue box where the initial material properties in the fit are specified, and the range of frequency over which the resonance spectrum will be fitted. If the resonance spectra has already been analysed, the previous results can be used as the initial material properties. Select Fit.
The progress of the fit will be updated on the graph. The fitting routine can be aborted at any time. The last best fit to the spectrum will be used to set results for an aborted fit.
Fitted material properties include an estimate of uncertainty.

When Analysis is Complete

When analysis is complete, the Analysis Results dialogue box appears. Here the various material properties determined from the length extensional mode are given.

The resonance spectrum for each selected fit in the Analysis Settings dialogue box will also be plotted over the original spectrum. The original data is displayed as open red circles, black solid lines, or both (o, ---). The complex material constant fit is displayed as a broken blue line (-----). The complex circuit constant fit is displayed as a broken green line (-----). The Van Dyke's circuit model fit is shown as a broken magenta line (-----).

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