Topology optimization applied to room acoustic problems and surface acoustic wave devices

The work of this PhD-project is concerned with the method of topology optimization1, which has been developed and used since the late eighties to optimize the material distribution of structures in order to minimize static compliance. Since then it has successfully been applied to a range of engineering fields such as mechanism design, fluid problems and photonic and phononic band-gap materials and structures [1,2]. In this project topology optimization is first applied to control acoustic properties in a room [3]. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized either by distribution of reflecting material in a design domain along the ceiling or by distribution of absorbing and reflecting material along all the walls for both 2D and 3D problems. It is also shown how the method can be used to design sound barriers. The main part of the project is concerned with simulation and optimization of surface acoustic wave (SAW) devices [4]. SAWs are for instance used in filters and resonators in mobile phones and to modulate light waves [5], and it is here essential to obtain waves with a high intensity, to direct the waves or to optimize the shape of the frequency response. To begin with, a 2D model of a Mach-Zehnder interferometer impacted by a SAW is considered and a parameter study of the geometry to get the biggest modulation of the light waves in the interferometer arms is performed. Then a 2D filter is modeled and optimized such that it reflects SAWs at certain frequencies or frequency ranges. To save computational time a 1.5D model will be developed, where an exponential decreasing waveform is introduced into the dept of the material, and the filter is then optimized based on this model. Later, the model will be extended to a 2.5D model in order to optimize more complicated SAW structures such as acoustic horns which focus the SAWs to a small area. [1] M. P. Bendsøe, O. Sigmund, “Topology optimization, theory, methods and applications”, Springer Verlag Berlin Heidelberg New York, 2nd edition, (2003). ISBN 3-540-42992-1. [2] J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends”, Applied Physics Letters, 84(12), 2022-2024 (2004) [3] M. B. Dühring, “Topology optimization for acoustic problems”, IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, Status and Perspectives, Series: Solid Mechanics and Its Applications , Vol. 137, M.P. Bendsoe, N. Olhoff and O. Sigmund (Eds.), Springer (2006). ISBN: 1-4020-4729-0. [4] K.-Y. Hashimoto, ``Surface acoustic wave devices in telecommunications modeling and simulation'', Springer, Berlin, (2000). ISBN 3-540-67232-X. [5] M. M. de Lima Jr and P. V. Santos, “Modulation of photonic structures by surface acoustic waves”, Rep. Prog. Phys., 68 1639-1701 (2005)