Multifrequency shape optimization of acoustic horn

Berggren, Martin; Bängtsson, Erik; Noreland, Daniel

doi:10.1016/b978-008044046-0.50541-8

Cited by 2 publications

(3 citation statements)

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“…An algorithmic difference from previous studies [7,8] is that we utilize better the least-squares structure of the problem and provide separately the gradients of the real and imaginary parts of the reflection coefficient to the optimization algorithm. This change, compared with previous practice, significantly lowered the number of iterations needed by the optimization algorithm.…”

Section: Discussionmentioning

confidence: 97%

“…The present article extends previous methods to consider also the far-field directivity properties, which are qualities as important as the raw efficiency of the horn. In contrast with previous studies [7,8], here the calculations are performed also for cylindrical symmetry.…”

Section: Introductionmentioning

confidence: 97%

“…Regarding acoustic waves, Noreland's Ph.D. thesis [6] introduces shape optimization ideas to the design of a trumpet flare in order to enhance the playability of the instrument. Methods to design the flare of a loudspeaker horn in order to minimize the back 1573 reflections or, equivalently, to maximize the transmission efficiency have been developed by the second author of this article and coworkers [7,8]. The studies showed that the transmission efficiency of a horn is very sensitive to the precise shape of the horn flare, and that it is possible by numerical optimization to design very efficient horns within a substantial frequency range.…”

Section: Introductionmentioning

confidence: 98%

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Optimization of an acoustic horn with respect to efficiency and directivity

Udawalpola

Berggren

2007

Numerical Meth Engineering

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SUMMARYWe consider the problem of designing an acoustic horn in order to efficiently transmit the incoming wave energy and favorably distribute the energy in the far field. A finite element solution of the Helmholtz equation, in planar or cylindrical symmetry, models the wave propagation. The transmission efficiency is monitored by measuring the back reflections into the feeding waveguide, and the far-field directivity pattern is computed using an integral expression known from scattering theory. The design problem is formulated as a non-linear least-squares problem, which is solved using a gradient-based algorithm, where the gradients are provided by solutions of the associated adjoint equations. The results demonstrate that this approach can generate horns with almost perfect transmission in a wide frequency band. Due to the improved transmission properties at the lower-frequency region, the optimization with respect to efficiency also generates improved far-field directivity patterns, that is, patterns that vary less with frequency. It is possible to obtain even more uniform directivity patterns by explicitly including directivity requirements in the optimization. However, those improvements in directivity seem to be associated with a substantial loss of efficiency.

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Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

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