Amplitude of the thickness vibrations of piezoelectric plates

In piezoelectric plates at resonance the amplitude direction of any thickness vibration mode generally varies with the distance from the center of the plate as well as the overtone number. Overtones of the same vibration mode do not have parallel amplitudes. As a result the existing definition of the vibration modes C, B and A must be reformulated and generalized. Numerical examples made for α-quartz show a substantial departure from the traditional model of the amplitude pattern which itself is valid only for the X-cut and rotated Y-cuts