LAMB WAVES IN MICROSTRUCTURED PLATES

The velocity dispersion of guided plate waves has been derived and studied in a plate composed of a coherent microstructured material. The calculated ultrasonic velocity dispersion arises from two sources: the conventional geometric Lamb wave dispersion due to the vanishing of tractions on the plate boundary, and microstructural dispersion due to the comparability of the ultrasonic wavelength and the microstructural dimension. The microstructure is assumed to take the form of laminations oriented vertically to the plate surfaces. The guided sound wave propagates in a direction parallel to the layer interfaces. Microstructural 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 equation, but yields additional frequency dependent terms which account for the dispersive nature of the original material system. It is found that the fundamental Lamb waves undergo significant modification as the ultrasonic wavelength approaches the microstructural dimension. For the 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 dependent on the ratio of plate thickness to microstructural dimension. A specific case is analysed numerically and physically, and limitations of the model are discussed in the context of real composite material systems.