PhD Defence at DTU Mechanical Engineering

PhD Defence 23rd September: Topology Optimization for Wave Propagation Problems with Experimental Validation

Wednesday 07 Sep 16


Rasmus Ellebæk Christiansen
DTU Mechanical Engineering
+4545 25 42 81

Rasmus E. Christiansen from DTU Mechanical Engineering defends his PhD, "Topology Optimization for Wave Propagation Problems with Experimental Validation", Friday 23rd September from 13:00 to 17:00. The defence takes place in Meeting Room S01, Building 101, at DTU. Professor Ole Sigmund from DTU Mechanical Engineering is main supervisor.

This Thesis treats the development and experimental validation of density-based topology optimization methods for wave propagation problems. Problems in the frequency regime where design dimensions are between approximately one fourth and ten wavelengths are considered. All examples treat problems from acoustics, however problems for TE or TM polarized electromagnetic waves and shear waves in solids in two dimensions may be treated using the proposed methods with minor modifications.

A brief introduction to wave problems and to density-based topology optimization is included. As is a brief discussion of the finite element method and a hybrid of a wave based method and the finite element method, used to discretize the model problems under consideration.

A short discussion of the benefits and drawbacks of applying the hybrid method compared to the finite element method, used in conjunction with topology optimization, is included. Preliminary results for novel preconditioners used in conjunction with the generalized minimal residual method for the iterative solution of wave problems, potentially suited for use with topology optimization, are discussed.

The development of an extension to an existing method, for assuring geometric robustness of designs created using density-based topology optimization, is presented. The method is applied to acoustic cavity design, and a significant improvement in the geometric robustness of several cavities demonstrated. Experimental validation of an acoustic cavity designed using the proposed method is provided.

A novel approach for designing meta material slabs with selectively tuned negative refractive behavior is outlined. Numerical examples demonstrating the behavior of a slab under different conditions is provided. Results from an experimental study demonstrating agreement with numerical predictions are presented.

Finally an approach for designing acoustic wave shaping devices is treated. Three examples of applications are presented, a directional sound emission device, a wave-splitting device and a flat focusing lens. Experimental results for the first two devices, demonstrating good agreement between measurements and the numerical predictions, are provided.