Computational analysis and design of phononic crystals
Immersed boundary analysis and level set based topology optimization
Sanne van den Boom (PhD candidate), Alejandro M. Aragón (supervisor), and Fred van Keulen (supervisor)
Phononic crystals have an interesting effect on waves traveling waves. For instance, they show bandgaps—ranges of frequencies that are prevented from propagating through the crystal. This is a useful property in many engineering applications, such as vibration isolation and energy harvesting. However, the design of these materials tailored to a specific application and frequency range is challenging, and as such, accurate and efficient modeling techniques are invaluable.
The performance of phononic crystals depends on both the topology of the inclusion and the lattice type, which is reflected in the shape of the PUC. Therefore, both the exterior and the interior boundaries are decoupled from the FE mesh. To that end, the PUC is analyzed in a fully immersed boundary setting, and Bloch-Floquet periodic boundary conditions are prescribed strongly on non-matching edges. With this approach the same performance as in standard FEM is achieved, while the geometry can be changed without changing the underlying analysis mesh.
As the behavior of phononic crystals is sensitive to the boundary description, the standard density-based topology optimization approaches become prohibitive, as extremely fine meshes would be required. Instead, the Interface-enriched Generalized Finite Element Method combined with level set-based topology optimization is more suitable for their numerical design than standard density based approaches.
- van den Boom, SJ, Aragón, AM, & van Keulen, F. "Mesh-Independent Design of Phononic Crystals Using an Advanced Finite Element Formulation." Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition. Volume 13: Acoustics, Vibration, and Wave Propagation. Phoenix, Arizona, USA. November 11–17, 2016.
- van den Boom, SJ, Abedi, R, van Keulen, F, Aragón, AM. On the importance of boundary smoothness in the computational design of phononic crystals (In preparation)