TY - JOUR

T1 - Far-field directivity of parametric loudspeaker arrays set on curved surfaces

AU - Guasch, Oriol

AU - Sánchez-Martín, Patricia

N1 - Funding Information:
This work has been supported by the BUILT2SPEC project, which has received funding from the European Union's Horizon 2020 Research and Innovation Program under Grant Agreement no. 637221. Moreover, the authors also acknowledge the support from the Ramon Llull University and the Generalitat de Catalunya through project 2017-URL-Proj-015.
Funding Information:
This work has been supported by the BUILT2SPEC project, which has received funding from the European Union’s Horizon 2020 Research and Innovation Program under Grant Agreement no. 637221 . Moreover, the authors also acknowledge the support from the Ramon Llull University and the Generalitat de Catalunya through project 2017-URL-Proj-015 .
Publisher Copyright:
© 2018 Elsevier Inc.

PY - 2018/8

Y1 - 2018/8

N2 - Parametric loudspeaker arrays comprise arrangements of piezoelectric ultrasonic transducers that emit highly directive audible sound, thanks to the nonlinear parametric array phenomenon. Most parametric loudspeakers consist of planar arrays of transducers though, lately, devices have been developed which involve their distribution on curved surfaces. In this work, we present an extension of the recently proposed convolution model for planar arrays to predict the far field directivity of curved parametric loudspeakers. An expression is first given to compute the audible secondary pressure field generated by a single ultrasonic transducer placed at any point on a general curved surface, and pointing in its normal direction. Assuming weak non-linearity, the total audible pressure produced by all transducers on the surface is then recovered from the superposition principle. As an application, we predict the far-field pressure generated by an omnidirectional parametric loudspeaker consisting of hundreds of ultrasonic transducers set on a sphere. A critical aspect for the performance of the omnidirectional source is that of finding a proper distribution for them on the spherical surface. Two options are analyzed: getting an optimal solution for a Fekete-like problem, and resorting to an equal-area partitioning scheme, which is more feasible for a practical construction of the source. Numerical simulations are carried out for both alternatives.

AB - Parametric loudspeaker arrays comprise arrangements of piezoelectric ultrasonic transducers that emit highly directive audible sound, thanks to the nonlinear parametric array phenomenon. Most parametric loudspeakers consist of planar arrays of transducers though, lately, devices have been developed which involve their distribution on curved surfaces. In this work, we present an extension of the recently proposed convolution model for planar arrays to predict the far field directivity of curved parametric loudspeakers. An expression is first given to compute the audible secondary pressure field generated by a single ultrasonic transducer placed at any point on a general curved surface, and pointing in its normal direction. Assuming weak non-linearity, the total audible pressure produced by all transducers on the surface is then recovered from the superposition principle. As an application, we predict the far-field pressure generated by an omnidirectional parametric loudspeaker consisting of hundreds of ultrasonic transducers set on a sphere. A critical aspect for the performance of the omnidirectional source is that of finding a proper distribution for them on the spherical surface. Two options are analyzed: getting an optimal solution for a Fekete-like problem, and resorting to an equal-area partitioning scheme, which is more feasible for a practical construction of the source. Numerical simulations are carried out for both alternatives.

KW - Curved surface

KW - Nonlinear acoustics

KW - Omnidirectional parametric loudspeaker

KW - Parametric acoustic array

KW - Parametric loudspeaker

KW - Westervelt equation

UR - http://www.scopus.com/inward/record.url?scp=85046360537&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2018.04.002

DO - 10.1016/j.apm.2018.04.002

M3 - Article

AN - SCOPUS:85046360537

SN - 0307-904X

VL - 60

SP - 721

EP - 738

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -