Propagation of acoustic waves in plates bordered with viscous liquid

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 A₀, symmetric Lamb wave S₆, and quasi-shear-horizontal wave QSH 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 η₁₁ and η ₄₄. It is found that the attenuation of the waves depends primarily on the shear component of viscosity η₄₄. The influence of expansion component η₁₁ is negligible. The attenuation per unit length is proportional to (η₄₄)^½ and f^1,3, where f is the frequency of the wave. Under identical conditions, the lowest value of attenuation is for the S₀ mode, while the highest is for the A₀ mode. For example, for h/λ=0.025 (h=plate thickness, λ=acoustic wavelength) and η₄₄=0.003 Ns/m², the attenuation in dB/cm at a frequency of 1 MHz for A ₀, S₀ and QSH₀ modes is 13.5, 0.024, and 0.073, respectively. The above results indicate that the S₀ 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