Pencil method in elastodynamics: application to ultrasonic field computation

The principles of pencil elastodynamics and, in more detail, some selected applications of pencil techniques to elastodynamics are described. It is shown how a systematic use of a matrix representation for the wave front curvature and for its transformations simplifies the handling of arbitrary pencils and, consequently, the field computations. Pencil matrix representations for the propagation into homogeneous solids made of isotropic or anisotropic media are derived. The use of matrix representations for pencil reflections on, or refractions through, arbitrarily curved interfaces, together with matrix representations for propagation into homogeneous media, allow us to derive an overall matrix formulation for elastodynamic propagation into complex heterogeneous structures. Combined with the classical Rayleigh integral to account for transducer diffraction effects, the proposed theory is applied to the prediction of ultrasonic fields radiated into complex structures by arbitrary transducers. Examples of interest for application to ultrasonic non-destructive testing are given.