Elastic Fields in Immersed Isotropic Solids from Phased Arrays: The Time Harmonic Case

Elastic fields in immersed isotropic solids from phased arrays are investigated theoretically in both far- and near-field regions for a variety of beams. The angular spectrum approach (ASA) is used here as a tool to evaluate both far-field beam patterns and near-fields in immersed solids with planar interfaces. Based on the angular spectra of the arrays in a fluid and the transmission coefficients of longitudinal and shear waves at the fluid/solid interface, the angular spectra in the immersed solid are obtained and used for analyzing far-field beam patterns and for constructing near-fields in the immersed solid. The numerical calculations are optimally implemented. Several examples are presented and analyzed of nonsteered and steered, nonfocused and focused, and longitudinal and transverse beams in copper submerged in water. Emphasis is placed on elastic fields from the oblique incidence of beams steered by arrays. One method of focusing a steered beam is investigated that, in phasing, takes into account refraction at the interface, so that the beam is directed at the desired angle in the solid. Analysis of far-field beam patterns in immersed solids obtained from the ASA is helpful for the design and development of arrays and for the adequate use of existing arrays in the immersion measurements in nondestructive evaluation.