Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder

Journal Article · Sat Nov 14 04:00:00 EST 2015 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.4935275· OSTI ID:22492918

Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θ{sub i}, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elements require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ε.

• OSTI ID: 22492918
• Journal Information: Journal of Applied Physics, Journal Name: Journal of Applied Physics Journal Issue: 18 Vol. 118; ISSN JAPIAU; ISSN 0021-8979
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
ASPECT RATIO
BEAMS
BOUNDARY CONDITIONS
COORDINATES
CROSS SECTIONS
CYLINDERS
CYLINDRICAL CONFIGURATION
EQUATIONS
EXACT SOLUTIONS
FLUIDS
INCIDENCE ANGLE
MATRIX ELEMENTS
PARTIAL WAVES
S MATRIX
SCATTERING
SERIES EXPANSION
SPHERICAL CONFIGURATION
SURFACES
WAVE PROPAGATION