In a previous post (#028) I showed how you can convert an evanescent sound field into a propagating one by using topology optimization. Now, I will briefly show that you can also use shape optimization for the same task. First, the unperturbed tube response:
It is clearly seen that at this particular frequency the sound field cannot propagate. With a proper shape optimization setup, this can be changed so that a plane wave emerges from perturbing part of the tube outline. I chose the same optimization domain length as in the previous post to have a fair comparison.
We see that now a plane wave propagates near the end of the tube. Just as with the topology optimization case, it is fascinating to see how these organic designs emerge from the underlying mathematics of objective functions, constraints, and all the choices made along the way.
I used a couple of so-called Bernstein polynomials to define the possible shapes, and so you can expect different results depending on which (and how many) polynomials you choose. There are plenty of pitfalls in this, like boundaries colliding, stretched mesh elements, and numerical issues, and so you should expect to invest some time in this, if it is relevant for you.
I plan to investigate the possibilities of shape optimization more in the future, and hope to show you more interesting cases soon.