Propagation of acoustic waves in plates bordered with viscous liquid

Abstract

This paper is concerned with the influence of a viscous liquid on the propagation of acoustic waves in thin plates of lithium niobate. The characteristics of the three lowest order wave modes that such a plate can support (zeroth order antisymmetric Lamb wave A/sub 0/, symmetric Lamb wave S/sub 6/, and quasi-shear-horizontal wave QSH/sub 6/) are investigated. It is assumed that the liquid is isotropic such that its viscous properties are described by two independent components of viscosity tensor /spl eta//sub 11/ and /spl eta//sub 44/. It is found that the attenuation of the waves depends primarily on the shear component of viscosity /spl eta//sub 44/. The influence of expansion component /spl eta//sub 11/ is negligible. The attenuation per unit length is proportional to (/spl eta//sub 44/)/sup 1/2 / and f/sup 1,3/, where f is the frequency of the wave. Under identical conditions, the lowest value of attenuation is for the S/sub 0/ mode, while the highest is for the A/sub 0/ mode. For example, for h//spl lambda/=0.025 (h=plate thickness, /spl lambda/=acoustic wavelength) and /spl eta//sub 44/=0.003 Ns/m/sup 2/, the attenuation in dB/cm at a frequency of 1 MHz for A/sub 0/, S/sub 0/ and QSH/sub 0/ modes is 13.5, 0.024, and 0.073, respectively. The above results indicate that the S/sub 0/ wave is most suitable for use in devices operating in contact with a viscous liquid. The results also show that by using the three different wave modes, one can develop a viscosity meter with a very wide measurable range of viscosity.