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A description of piezoelectric effect in non‐polar materials taking into account the quadrupole moments
Author(s) -
Ivanova Elena A.,
Kolpakov Yaroslav E.
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400255
Subject(s) - quadrupole , piezoelectricity , dipole , physics , polar , moduli , condensed matter physics , dispersion relation , classical mechanics , materials science , quantum mechanics , acoustics
A method of the description of piezoelectric effect in non‐polar materials is suggested. This method is based on the model of unit cell possessing a non‐zero quadrupole moment and the zero dipole moment. The suggested theory contains several additional material tensors. A comparison of the suggested theory with the classical theory of piezoelectricity is carried out. The structure of the additional material tensors is determined for the crystal lattice with the hexagonal crystal symmetry of quartz. An analysis of dispersion relations is carried out. This analysis reveals that the quadrupole moment tensor has a qualitative influence on the behavior of solution. Namely, the quadrupole moments cause rather the redistribution of energy between the waves of different type than the wave damping. A method of determination of the additional material moduli is suggested. The method consists in using the dispersion relations containing the unknown material moduli and the experimental data on attenuation factor versus frequency.