LAMB WAVES IN MICROSTRUCTURED PLATES

The velocity dispersion of guided plate waves has been derived and stu died in a plate composed of a coherent microstructured material. The c alculated ultrasonic velocity dispersion arises from two sources: the conventional geometric Lamb wave dispersion due to the vanishing of tr actions on the plate boundary, and microstructural dispersion due to t he comparability of the ultrasonic wavelength and the microstructural dimension. The microstructure is assumed to take the form of laminatio ns oriented vertically to the plate surfaces. The guided sound wave pr opagates in a direction parallel to the layer interfaces. Microstructu ral dispersion is treated by the continuum mixture approach, where the spatial dependence of field variables normal to the lamina interfaces has been approximated by averaging these quantities across the lamina thickness. This procedure reduces the dimensionality of the wave equa tion, but yields additional frequency dependent terms which account fo r the dispersive nature of the original material system. It is found t hat the fundamental Lamb waves undergo significant modification as the ultrasonic wavelength approaches the microstructural dimension. For t he symmetric mode, this effect consists of a much more rapid decrease in the Lamb wave phase velocity as it approaches the Rayleigh velocity of the slower medium, instead of the mixture value. The antisymmetric mode displays a broad maximum, whose frequency of occurrence is depen dent on the ratio of plate thickness to microstructural dimension. A s pecific case is analysed numerically and physically, and limitations o f the model are discussed in the context of real composite material sy stems.