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

## Abstract

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-sphericalmore »

- Authors:

- Chevron, Area 52 Technology, ETC, Santa Fe, New Mexico 87508 (United States)

- Publication Date:

- OSTI Identifier:
- 22492918

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Applied Physics

- Additional Journal Information:
- Journal Volume: 118; Journal Issue: 18; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-8979

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 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

### Citation Formats

```
Mitri, F. G., E-mail: F.G.Mitri@ieee.org.
```*Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder*. United States: N. p., 2015.
Web. doi:10.1063/1.4935275.

```
Mitri, F. G., E-mail: F.G.Mitri@ieee.org.
```*Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder*. United States. https://doi.org/10.1063/1.4935275

```
Mitri, F. G., E-mail: F.G.Mitri@ieee.org. Sat .
"Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder". United States. https://doi.org/10.1063/1.4935275.
```

```
@article{osti_22492918,
```

title = {Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder},

author = {Mitri, F. G., E-mail: F.G.Mitri@ieee.org},

abstractNote = {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.},

doi = {10.1063/1.4935275},

url = {https://www.osti.gov/biblio/22492918},
journal = {Journal of Applied Physics},

issn = {0021-8979},

number = 18,

volume = 118,

place = {United States},

year = {2015},

month = {11}

}