Вплив п’єзоелектричного ефекту на поширення хвиль лемба у пластинах кристалів класу 6mm
Abstract
INFLUENCE OF PIEZOELECTRIC EFFECT ON THE PROPAGATION OF LAMB WAVES IN PLATES OF THE CLASS 6mm CRYSTALS
P. Ilyin
For non-destructive testing of the new materials that obtained in the form of thin layers or plates, ultrasonic Lamb waves are used. The parameters of these waves depend on the elastic properties of the material, especially near the critical frequencies, where there is a strong frequency dispersion of wave velocities. The influence of piezoelectric properties of material on the phase velocity of Lamb waves also increases when approaching the critical frequencies.
The aim of this work was to study the influence of piezoelectric effect on the properties of Lamb waves near cutoff frequencies of the symmetric and antisymmetric modes, in particular their dispersion in crystals of 6mm symmetry.
The propagation of Lamb waves in the direction of the axis of the sixth order in plates of crystals of 6mm symmetry was considered in the presence of the piezoelectric effect. For this case the dispersion equation of Lamb waves, have been obtained previously. These equations are transcendental and in arbitrary cases they can be solved only by numerical methods.
In this work the solution of these equations was carried out near the cut frequencies by analytical methods, approximately. Used the fact that when approaching the cutoff frequency the phase velocity of the corresponding Lamb mode tends to infinity and the wave number in the cutoff frequency region tends to zero. This gave the opportunity to expand trigonometric functions that are included in the dispersion equation, in a Taylorseries in a neighborhood of the cutoff frequencies and to obtain approximate dispersion equations that give the relationship between dimensionless wave number q and dimensionless frequency. For cases q<<1 the coefficients at q and q2 were calculated with the accuracy to terms proportional to the square of the electromechanical coupling coefficient.
The approximate dispersion equations for symmetric and antisymmetric Lamb waves were obtained. From their decision one can see that the antisymmetric modes that exist at a cutoff frequency as the shear wave, and symmetrical modes that exist at a cutoff frequency as the longitudinal waves, due to the piezoelectric effect can exist at frequencies below cutoff frequency and to have oppositely directed phase and group velocities. Previously, these properties of Lamb waves in plates of crystals of 6mm symmetry were not known.
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