The problem of the frequency-dependent directivity of ordinary loudspeaker diaphragms is addressed by formulating a numerical shell model of the diaphragm. In this model, a change in material and geometrical properties, leading to a change in directivity, is possible, and an optimization is performed in order to change the directivity toward a desired behavior.
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https://aes2.org/publications/elibrary-page/?id=6627
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