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Some of the terms in the magnitude and the phase of the voltage FRF can be put into dimensionless form to give
п /аЛ _1 /(2£г + иг (1 + Уг))ш – игш3
Ф (ш) = – sgn 2-І – tan —————————– :—– „2п…——————
2 вг ) 1 – ш2 (1 + 2игКг)
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Similarly, the magnitude and the phase of the tip displacement FRF become
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Ur = RlCepq &r |
(5.13) |
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ё2 |
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Yr = „ eq 2 Cp &r2 |
(5.14) |
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& |
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& = —– |
(5.15) |
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&r |
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fr (x) = ar Фг (x) |
(5.16) |
where Ur is the dimensionless resistance, Yr is the dimensionless electromechanical coupling factor, & is the dimensionless excitation frequency, and fr(x) is the dimensionless modal mechanical forcing function. Note that the voltage modulus given by Equation (5.9) is dimensional due to ar /Qr (with units of V s2/m) whereas the tip displacement modulus given by Equation (5.11) is dimensional due to 1 /&2 (and has units of s2).
