Resonance modes in plates vibrating in thickness

Abstract

In anisotropic (piezoelectric) plates at resonance the amplitude direction of any thickness vibration generally varies with the distance from the centre of the plate. Amplitudes of the extentional and two transverse vibration modes are not perpendicular and, for overtones of the same vibration mode, are not parallel. The common feature of vibrations belonging to the same mode is a similar rather than identical amplitude direction. The amplitude at many nodal locations becomes nonzero and the amximum amplitude is not always at the plate surface. These phenomena are described analytically and subsequently illustrated by numerical examples made for α-quartz. They show that the amplitude direction may depart from the 'classical' constant direction by tens of degrees. The classical amplitude pattern with amplitudes of constant direction can be found only in isolated cases. Insofar as the response of resonance states to changes of temperature, externally applied pressure, or electric field, depends on the amplitude direction, differences must be expected in the behaviour of overtones belonging to the same vibration mode. This appears to be borne out by experimental results.