Mode Shape Normalisation

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It is useful to know how to normalise magnitude and phase from a mode shape so that it can be compared directly with a laser vibrometer measurement. This can be done in a few basic steps using the data command:

  1. Convert displacement data from real/imaginary to magnitude/phase
  2. Convert voltage data from real/imaginary to magnitude/phase
  3. Use #get command to obtain magnitude and phase values for normalisation
  4. Convert to displacement per volt
  5. Correct phase variation between displacement 

The resulting output is the model geometry displayed with a colour scale relating to the values of displacement for a drive signal of 1 V:

These displacement measurements can then be easily scaled for different drive signals.

Example Code

/* Convert X Disp from real/imag to mag/phase
polr shap/xdsp:r1 shap/xdsp:i1 to shap/xdsp:m1 shap/xdsp:p1
polr shap/ydsp:r1 shap/ydsp:i1 to shap/ydsp:m1 shap/ydsp:p1
/* Convert voltage data from real/imag to mag/phase
polr shap/pize:r1 shap/pize:i1 to shap/pize:m1 shap/pize:p1
/* Get voltage mag and phase value for normalisation symb #get { valmpz1 } array shap/pize:m1 1 1
symb #get { valppz1 } array shap/pize:p1 1 1
/* Convert to displacement/volt
math shap/xdsp:m1 = { shap/xdsp:m1 } / $valmpz1
math shap/ydsp:m1 = { shap/ydsp:m1 } / $valmpz1

/* Correct phase variation between displacement
math shap/xdsp:p1 = { shap/xdsp:p1 } - $valppz1
math shap/ydsp:p1 = { shap/ydsp:p1 } - $valppz1
end

/* Plot Mode Shape measured in Y Displacement/Volt
grph
nvew 1
pset sttl '1MHz - Y Displacement/Volt Plot'
plot shap/ydsp:m1
end

Example Files

The following is an example of how to normalise a mode shape for a 2D PZT Disc:

 
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