New modelling for piezoceramic characterization

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Abstract
Standards on piezoelectricity1 describe the analysis of vibration on piezoelectric materials having simple geometrical shapes. The results are based on linear piezoelectricity and resonance modes are treated as non-coupled vibration modes.2 However, in general, real materials involve coupled modes due to both piezoelectricity and elasticity effects. In addition, they have geometrical dimensions which are of the same order of magnitude. Therefore, the one-dimensional approaches no longer apply. The general constitutive equations are so complicated that the direct resolution is quite impossible. For piezoceramic, coordinate axes are pure mode propagation directions, that is mechanical displacements along these axes are only related to a single coordinate. In this case, the constitutive equations reduce and the three dimensional determination of vibrational modes becomes possible.

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