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^{1,2,a)}, Antonio Uris

^{1}and Francisco Meseguer

^{1,2}

### Abstract

The radiation of sound by a periodically corrugated rigid piston is explored using theoretical and numerical approaches and compared with the radiation of flat rigid piston. The depth and the period of the corrugation are considered to be comparable with the wavelength in the surrounding fluid. Radiation enhancement is predicted due to cavity resonances and coherent diffraction. In addition, broad regions of low radiation efficiency are observed. Both effects could have an impact in acoustic transducers technology, either to increase the piston radiated power or to create a source of evanescent acoustic waves. The possibilities offered by this strategy in the nonlinear acoustic regime are also briefly discussed.

This work has been supported by the Spanish MICINN (MAT2010-16879, Consolider CSD2007-00046 and Universitat Politecnica de Valencia (PAID-06-10-1839). We gratefully acknowledge the valuable help of Javier García de Abajo in the development of the modal model.

### Key Topics

- Transducers
- 8.0
- Acoustic waves
- 6.0
- Acoustic transducers
- 4.0
- Finite element methods
- 4.0
- Sound pressure
- 4.0

## Figures

Diagrams showing the geometry and the relevant variables and constants of the problem for (a) flat rigid piston and (b) for a periodically corrugated rigid piston. The radiated sound power is labeled as and for each case.

Diagrams showing the geometry and the relevant variables and constants of the problem for (a) flat rigid piston and (b) for a periodically corrugated rigid piston. The radiated sound power is labeled as and for each case.

Time averaged quadratic pressure field ( in normalized units) of a flat (a) and (b) a corrugated piston having ten cavities (), *d* = 0.3 *a*, and *h* = 0.71 *a* at a λ = 0.9 (c) NPL in (dB) along *z/D* at the radiation axis.

Time averaged quadratic pressure field ( in normalized units) of a flat (a) and (b) a corrugated piston having ten cavities (), *d* = 0.3 *a*, and *h* = 0.71 *a* at a λ = 0.9 (c) NPL in (dB) along *z/D* at the radiation axis.

(a) Radiation efficiency in (dB) of a corrugated piston with proportions *h/a* = 1.71 and a hole filling fraction *f* = 0.3 calculated using different models (see labels) as a function of . (b) Magnitude (solid curve, left vertical axis) and phase (dashed curve, right vertical axis) of the average velocity at the aperture entrance calculated with the two-dimensional modal expansion as a function of .

(a) Radiation efficiency in (dB) of a corrugated piston with proportions *h/a* = 1.71 and a hole filling fraction *f* = 0.3 calculated using different models (see labels) as a function of . (b) Magnitude (solid curve, left vertical axis) and phase (dashed curve, right vertical axis) of the average velocity at the aperture entrance calculated with the two-dimensional modal expansion as a function of .

Radiation efficiency in (dB) as a function of of a corrugated piston (a) having *f* = 0.1 for different *h/a* ratios and (b) for fixed *h/a* = 0.71 and different hole filling fractions *f*.

Radiation efficiency in (dB) as a function of of a corrugated piston (a) having *f* = 0.1 for different *h/a* ratios and (b) for fixed *h/a* = 0.71 and different hole filling fractions *f*.

(a) Radiation efficiency in (dB) as a function of for a corrugation having *h/a* = 0.71 and *f* = 0.52 calculated for infinite and finite pistons. The arrow shows the point at which the fields in (b) and (c) have been calculated. Normalized pressure level fields in (dB) for a (b) corrugated and (c) flat piston at .

(a) Radiation efficiency in (dB) as a function of for a corrugation having *h/a* = 0.71 and *f* = 0.52 calculated for infinite and finite pistons. The arrow shows the point at which the fields in (b) and (c) have been calculated. Normalized pressure level fields in (dB) for a (b) corrugated and (c) flat piston at .

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