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Abstract

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EXPERIMENTAL STUDY OF BACKWARD LAMB WAVES IN LITHIUM NIOBATE CRYSTAL PLATE

P.P. Ilyin

Abstract. Backward elastic waves have oppositely directed phase and group velocity. They are interesting to research due to some of their unusual properties. Backward elastic waves have promise for use in acoustoelectronics and non-destructive testing because they are able to have a wide range of the phase velocity values with insignificant dispersion of group velocity. Recently, lot of attention has been given to elastic waves those have zero group velocity and the finite phase velocity. Such waves are intermediate between the backward wave and forward wave (in which direction of the phase and group velocities coincide). A necessary condition for the existence of the wave with zero group velocity is the existence of the backward wave. Therefore, the study of backward elastic waves is necessary to determine of the existence and properties of waves with zero group velocity.

The propagation of Lamb waves in the Y-cut plate of lithium niobate was studied. The plate had a thickness of 2h = 750 microns. Under wave propagation along the Z axis the fours Lamb mode was studied. That mode had the cutoff frequency at which the plate thickness equaled to one and a half length of the shear waves. The velocity of forward wave of this mode was measured too. In forward wave directions of the phase and group velocities coincide. Theoretical calculations indicated the possibility of a backward wave existence in such plates.

Excitement and registration of elastic waves were carried out with using the piezoelectric properties of the material of plate. The high-frequency voltage to excite Lamb waves was applied to metal electrodes deposited symmetrically on opposite sides of the plate. Lamb wave propagation in piezoelectric materials was accompanied by a high-frequency electric field. Thus the registration of the waves was carried out with movable electrode that could move along the plate with a micrometer screw. The research was carried out at a frequency range of 8-9 MHz with using radio pulses which duration was about 10 microseconds.

For the measurements of phase velocity the phase method of variable base was used. The changing of the distance between the source and receiver of wave caused a change of wave propagation time and phase of its vibrations at the receiver. The changes of the distance for one wavelength corresponded to the phase change to .The relative measurement error of wavelength and phase velocity was less than 1%. The directions of energy transfer by waves and group velocity coincided, therefor real waves had positive group velocity. The backward waves had negative phase velocity which directed to the source of waves. The direction and the sign of phase velocity were observed when the distance between the source and the receiver of waves was varied by an amount less than a half of the wavelength. The increasing of the distance resulted in decreasing of phase difference between high-frequency voltage on wave source and wave receiver in case of backward wave, and resulted in increasing of phase difference in case of forward wave.

The measurement of the group velocity was carried out by the phase method of variable frequency. The relative error in the measuring of the group velocity was about 1%.

The measurement results of the frequency dependence of the phase and group velocities of the backward and forward waves of fourth Lamb mode are presented. The dependence of the velocity on the dimensionless parameter fh, where f ?? frequency waves, h ?? half the thickness of the plates, is shown in the figures. The phase velocity of the backward wave has strong frequency dispersion and its value in the investigated frequency range varies m/s. The value of the forward wave phase velocity in the investigated frequency range is m/s.

It is experimentally confirmed that fourth Lamb mode in the plate of lithium niobate is backward wave. Thus at the certain frequency a wave corresponding to this mode can have zero group velocity at the finite value of the phase velocity. The backward wave has a strong frequency dispersion of phase velocity. The group velocity dispersion has small value.