Acoustic field radiated into a transversely isotropic solid from a small aperture spherical surface

The acoustic field modelling reported in this paper finds application in the design of a scanning probe tip for measuring the near-surface elastic properties of solids and surface structures at high frequencies and with high spatial resolution. The underlying concept is for a longitudinally polarized pulse to be launched from a spherically-shaped portion of the upper surface of the pyramidal or conical shaped tip, and focused towards the narrow lower end. The change in the reflectivity when the narrow end is brought into contact with a solid will provide a measure of the local frequency dependent compliance of that solid. The calculations assume the material from which the tip is fabricated to be transversely isotropic, with symmetry axis coinciding with the axis of the tip. The main issue addressed in this paper is the role of the curvature of the radiating surface and anisotropy of the medium in determining the focal length and focal spread of the radiated field. Two complementary approaches are taken, firstly the discretization of the equations of motion on an irregular mesh of around 3 × 105 triangular elements and solution using the commercial FE package ABAQUS/Explicit, and secondly an analytical approach based on ray tracing and a Green’s function method exploiting the angular spectrum method and stationary phase approximation in its evaluation. Consistency is achieved between these approaches regarding the characteristics of the focal region. With the combination of the two approaches it is thus possible to model the wave field from low frequencies, where the FE method is computationally economical and able to handle complex geometries, to high frequencies, where advantage increasingly lies with ray tracing and the Green’s function method.

► FE, ray and Green’s function methods are applied to elastic wave field modeling.
► Radiation by a spherical surface into a transversely isotropic solid is determined.
► Expressions for the focal length and focal spread are obtained.
► The results are applicable to a scanning probe tip for measuring elastic properties.