Structural vs. Acustic Piezoelctric Loupspeaker Optimization

Here comes my own talk from WCSMO-8. It deals with the topology optimization of a piezoelectric loudspeaker. I consider the full coupling with acoustics and a pure structural approximation. Both cases are compared and it turns out, that for my model, the structural approximation does not hold for most cases as the objective function favours vibrational patterns that actually lead to acoustic short circuits. What I do is actually to load the final topologies from the structural optimization and evaluate the sound power with a fully coupled simulation.

This might also be the first publication about a fully piezoelectric-mechanical-acoustic coupled loudspeaker. The interesting thing is that the structural eigenmodes both cannot be excited by a full piezoelectric patch and also would result in acoustic short circuits.

For a weakly coupled form, using boundary elements, Nils Olhoff and Jianbin Du presented "Minimization of Sound Pressure in the Acoustic Field Generated by Vibrating Structures Using Topology Optimization" (#1396).

You can have a look to my talk (download talk)

Topology Optimization of a Piezoelectric Loudspeaker Coupled with the Acoustic Domain

View more Microsoft Word documents from fwein.

and download the conference proceedings paper. The title is "Topology Optimization of a Piezoelectric Loudspeaker Coupled with the Acoustic Domain" (#1230) by Fabian Wein, Manfred Kaltenbacher, Fabian Schury, Eberhard Baensch and Guenter Leugering.

CU@WCSMO-8 in Lissbon

Hi topology optimizers outside,

thanks to FEEDJIT I know that indeed some guys are reading my blog. In case you are topology optimizers and
also participate at the WCSMO ("World congress" sounds nice :)), you can meet me at my session 19.1, wednesday (I'm the last 9:30-9:50). 19 is about "Multiphysics Topology Optimization".

I talk about a comparisson of topopolgy optimization within the acoustic domain and the pure structural approximation. Clearly via piezoelectric excitation and as common for me, I have no penalization, no volume constraint and achieve quite good 0-1 results w/o any regularization. I also speak about the vibrational patterns: the mechanical eigenmodes, the piezoelectric excitation of these and the link to acoustic short circuits.

It would be actually nice to finally learn to know a reader of my blog. :)

Math riddle

There is a lot going on at the moment - time for a short break. :)

I got this little riddle from a colleague, he told me it's a first semester math student standard.

We start with

a = b

multiplying with a we get

a^2 = ab

substracting b^2

a^2 - b^2 = ab - b^2

this is

(a+b) (a-b) = (a-b) b

now cancelling (a-b)

(a+b) = b

and as a=b (first line!)

a+a = a

hence 2a = a

or 2 = 1


Funny, isn't it :)
Have fun searching for the wrong statement.

Down to the labs

There is more good news :)

It appears that we made an invention (when this is defined by something which
get's patented). Currently we construct an experimental prototype (which is real
hardware). It takes a lot of time but it is also exiting and makes a lot of fun. The details evolve along construction in discussion with the (excellent) mechanic of my
engineering chair. Next week we will start meassurements - and if all works fine
we'll try to apply for a patent.

I learned some mechanical basics before I started my first study (engineering) and
it remindes me to that times.

What is really cool, if the stuff works - it's found by optimization. Engineers are
working for quite some time to solve the problem - maybe the algorithm found it (it's not that intuitive in the first glance) ... well, let's see.

Paper accepted

Lucky day today :)

Some time ago I got back the review of our first paper. I'm currently working on the next version, taking the comments of the reviewer into account.

What I did not post, is that we also submitted a second paper dealing with the dynamic optimization. It was submitted along the OIPE workshop. Here is the preprint. The comments of the two reviewers came today and were actually quite good (twice an "eight"). I was escpecially happy about the comment "The detailed discussion is nice." as a lot of effert went into that paper.

After working in the comments the paper will appear in a special issue (optimization and inverse problems) of the International Journal of Applied Electromagnetics and Mechanics IJAEM.

What is the paper about? It does dynamic optimization of the piezoelectric loudspeaker:



Brown is the thin metal plate (think of the "membrane" of a loudspeaker, even if the term is in this case not correct) which is excited by a thin piezoelectric layer (blue). We search for the best topology of the piezoelectric layer.

What needs to be clearified in the first paper, is that we need no volume constraint. Hence, when doing a parameter study optimizing for many frequencies from 20 to 2000 Hz



We can check what the optimal volume is and if it is really "black and white" enough. This is the special intrinsic piezoelectric feature we found and what needs to expressed in more detail for the revision of the first paper.



A typical example (800 Hz) is the following picture where blue means "no piezoelectric material" but brown means, "yes - place the pizeo here".




The paper discusses some interesting ressonance issues of piezoelectric optimization (it's special there!) and does also multiple frequency optimization. But that's much to much for a blog posting.

Books about Topology Optimization

When it comes about the SIMP method, the standard book is clearly
Bendsoe, M.P. and Sigmund, O.; Topology Optimization: Theory, Methods, and Applications; Springer; 2003 (scholar.google, amazon). Bendsoe and Sigmund are the godfathers of modern SIMP and their review book like work gives a lot of insight into various achievements and limits of the method. On the other side it is not that appropriate to hand to a studendt to get a glimpse about SIMP, especially on the basics and backgrounds.

Since a couple of weeks only there is another book available:
Christensen, P.W. and Klarbring, A.; An Introduction to Structural Optimization; Springer; 2008 (scholar.google, amazon). It covers truss optimization, SIMP but also the necessary basics in optimization mathematics (e.g. convexity, MMA, ...). I would say it is ideal for studens of computational engineering. For math students the proofs are missing but "normal" engineers should not fear math language, albeit the content is appropiate for them. The book has even exercies and gives a very good introduction to the subject.

Concerning the covered content: Background and exercises versus review like collection of applications, do these books complement each other almost ideally. One (engineer) should just read Christensen and Klarbring prior to Bendsoe and Sigmund (after browsing the later's applications as motivation :)).

Serguei Nazarov - The Big Fish

Prof. Nazarov was invited to Erlangen 2 weeks before. Within my project topology optimization is also done via topology gradients, mathematical hard core where pure mathematicians meet the applied ones. I'm an engineer, I do SIMP and it is hard for me to understand what the mathematicians do (I want to start another try for a functinal analysis book the next weeks).

Anyway I was asked to give a short talk and present the piezoelectric-mechanical-acoustic coupled PDE from an practical engineering point of view (application, meshing, boundary conditions, ...). The talk was to be given for Prof. Nazarov, I never heard of. So I googled and it was interesting what I found.

First the image from his website in Russia


He is an expert on asymtotical extensios. On His page are links to his 13 books!! and 366 papers!! There is really nothing to add beside that he is a nice and funny guy. :)