Excess attenuation of leaky Lamb waves due to viscous fluid loading

In two recent papers [J. Acoust. Soc. Am. 97, 3191–3193 (1995) and 98, 1057–1064 (1995)], Zhu and Wu presented an analytical technique to assess the effect of viscous fluid loading on the propagation properties of Rayleigh and Lamb waves in fluid-loaded solids. They modeled the viscous fluid as a hypothetical isotropic solid having rigidity c55=−iωη, where η denotes the viscosity of the fluid and ω is the angular frequency. In this way, the vorticity mode associated with the viscosity of the fluid is formally described as the shear-mode in the fictitious solid. In this paper this technique is further developed by removing certain inconsistencies that unnecessarily reduce the accuracy and the range of validity of Zhu and Wu’s results. By properly accounting for viscous effects on the bulk compressional wave in the fluid and applying a rigorous treatment of the field equations and boundary conditions, the exact dispersion equations that are not limited to low frequencies and viscosities are derived. Examples of these results are presented to illustrate the effect of fluid viscosity on the lowest-order symmetric and antisymmetric Lamb modes. One interesting feature revealed by these calculations is the presence of a sharp minimum in the viscosity induced attenuation of the lowest-order symmetric mode of thin plates either immersed in or coated with a viscous fluid. This minimum occurs at a particular frequency where the otherwise elliptical polarization of the surface vibration becomes linearly polarized in the normal direction.