Geometric approximation of radiation stress projections for canonical objects

Modulated ultrasonic radiation pressure facilitates the selective excitation of modes of objects through modulation of appropriate surface stress projections [P. L. Marston and R. E. Apfel, J. Acoust. Soc. Am. 67, 27–37 (1980)]. For some large objects, it can be impractical to evaluate the needed stress projections using standard analytical or computational methods. For highly reflecting objects geometric approximations may provide useful insight into the relevant stress projections. The simplest projection gives the translational radiation force on the object. In that case, ray analysis of the far-field scattering was shown to recover the radiation force on large perfectly reflecting spheres in plane waves [P. L. Marston, J. Acoust. Soc. Am. 120, 3518–3524 (2006)]. In the present research, the appropriate force limit is also recovered through integrating a geometrically approximated local stress projection on the object’s surface. Appropriate limiting forces for other canonical objects or situations involving illumination by beams are also found to be recovered using geometrical methods. It was helpful to generalize some prior geometrical results [P. L. Marston, J. Acoust. Soc. Am. 121, 753–758 (2007)] for scattering by perfectly reflecting spheres. [Work supported by ONR.]