Derivation of acoustoelastic Lamb wave dispersion curves in anisotropic plates at the initial and natural frames of reference

The propagation speed of ultrasonic waves in pre-stressed media can be evaluated either at the natural or initial frames of reference. In this paper general equations that can be applied to the partial wave technique are presented in order to obtain the dispersion spectra of acoustoelastic Lamb waves in anisotropic plates in either frame of reference. Employing these equations, dispersion curves for the fundamental modes in a pre-stressed transversely isotropic aluminum plate were numerically obtained in both reference frames under longitudinal and transverse loading with the material transverse axis along each of the Cartesian directions, as well as the propagation along a non-principal direction. Results confirm that due to the material natural anisotropy, the speed variation depends not only on the pre-stress direction but also on the material orientation as well as on the polarization of the propagating mode. Similar to bulk waves, the relationship between the speed at the natural and initial frames is a function of the load direction.

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