ACOUSTIC RADIATION FORCE AND TORQUE ON A SOLID ELLIPTIC CYLINDER

Abstract

Exact expressions for the acoustic radiation torque and force components experienced by elastic cylinders of elliptic cross-section immersed in ideal fluids and placed in a progressive or standing wave field is developed. The classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop analytical expressions in the form of infinite series involving Mathieu and modified Mathieu functions. The complications arising due to the nonorthogonality of angular Mathieu functions corresponding with distinct wave numbers as well as problems associated with the appearance of additional angular dependent terms in the boundary conditions are all avoided in an elegant manner by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. Numerical calculations of the radiation force and torque function amplitudes are performed in a wide range of frequencies and cross-sectional eccentricities for a stainless steel cylinder submerged in water. Particular attention is paid to assessment of the effects of cross-sectional ellipticity as well as incident field asymmetry on the acoustic radiation force/torque acting on the elliptical cylinder. Limiting case involving an elastic circular or elliptic cylinder in an ideal fluid is considered and fair agreements with well-known solutions are established.