A framework for computing directivities for ultrasonic sources in generally anisotropic, multi-layered media

The knowledge of the directivity of ultrasonic sources is an important element in the design of non-destructive evaluation inspection. The commonly used directivity model of piezoelectric devices is the superposition of out-of-plane force monopoles on the stress-free surface of an isotropic elastic half-space. However, this does not cover a growing range of ultrasonic generation scenarios, as new ultrasonic technologies such as laser ultrasound (LU) emerges, and the need for inspection of materials such as carbon fibre reinforced polymers (CFRPs) rises. A directivity calculation framework based on the reciprocity theorem is developed in the current paper, which accommodates various combinations of source types, material properties, and boundary conditions, for example, a localised heating under a surface layer over an anisotropic half-space. The calculation is applicable to materials with weak anisotropy or wave modes that do not have cuspoidal wavefronts, and was validated with finite element models on key representative cases. The analytical solution for LU excitation in a CFRP sample also shows a good fit to the experimentally measured directivity of the quasi-longitudinal wave mode.