Abstract
The propagation of ultrasonic waves in a liquid layer sandwiched between rigid bodies is equivalent to the propagation of SH waves in an elastic plate as pointed out by Sato. Hence the lowest branch of a dispersion equation is nondispersive and can be utilized to advantage in ultrasonic information processing devices. The distribution of energy in a cross section is uniform for low frequencies at which only the lowest branch can propagate and suitable for ultrasonic imaging. Real solid is not rigid but elastic. The present paper examines the effect of elasticity of solid bodies. Dispersion equations are derived for symmetric and antisymmetric modes. Dispersion curves(Fig. 2), phase velocity(Fig. 3) and group velocity(Fig. 4), displacement(Figs. 6〜9) and energy flow distribution (Figs. 10〜13) in a cross section are numerically calculated for the first few modes in a water layer sandwiched between two sheets of glass. An examination of these results shows that:(1) The lowest branch has now an imaginary wave number along the direction perpendicular to boundaries, but essentially retains the features in the case of rigid bodies. The velocity measured by a light diffraction method shows few dispersion as predicted. (2) Each higher branch has a cut-off frequency when its phase velocity becomes equal to the shear velocity of solid bodies. (3) The overall view of dispersion curves can be interpreted as a result of coupling between the branches in case of rigid bodies and those of the surface waves on solid boundaries.
