WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

The optimization algorithm employs repeated material redistributions based on
analytical sensitivity analysis and mathematical programming. In this work we develop
continuous material interpolation functions using a simple 1D model, and use the
method to design a reflection chamber that minimizes the transmitted wave in a designated
frequency range. The frequency range optimization is facilitated by computing
fast frequency sweeps to identify the most critical frequencies.
Further work will include multi-physics modelling in order to study coupled problems,
e.g. combined fluid flow and acoustic wave propagation or fluid-structure interaction.
This work was supported by the Danish Technical Research Council (FTP).
REFERENCES
[1] Bängtsson, E., Noreland, D. and Berggren, M., “Shape optimization of an acoustic
horn”, Computer Methods in Applied Mechanics and Engineering, 2003, 192:11–
12, 1533–1571.
[2] Bendsøe, M.P. and Kikuchi, N., “Generating optimal topologies in structural design
using a homogenization method”, Computer Methods in Applied Mechanics
and Engineering, 1988, 71:2, 197–224.
[3] Sigmund, O. and Jensen, J.S., “Design of acoustic devices by topology optimization”,
Short papers of the 5th World Congress on Structural and Multidisciplinary
Optimization WCSMO5, 2003, 267–268.
[4] Sigmund, O., Jensen, J.S., Gersborg-Hansen, A. and Haber, R. B., “Topology
optimization in wave-propagation and flow problems”, Proceedings of Warsaw
International Seminar on Design and Optimal Modelling WISDOM, 2004, 45–
54.
[5] Bendsøe, M.P. and Sigmund, O., “Topology Optimization: Theory, Methods and
Applications”, Springer Verlag, Berlin, 2003.
[6] Olesen, L.H., Okkels, F. and Bruus, H., “A high-level programming-language
implementation of topology optimization applied to steady-state Navier-Stokes
flow”, International Journal for Numerical Methods in Engineering, 2004, submitted.
[7] Svanberg, K., “The Method of Moving Asymptotes - A New Method for Structural
Optimization”, International Journal for Numerical Methods in Engineering,
1987, 24, 359–373.
[8] Jensen, J.S., Sigmund, O., “Topology optimization of photonic crystal structures:
A high-bandwidth low-loss T-junction waveguide”, Journal of the Optical Society
of America B, 2005, to appear.
8