Reduced-order topology optimization of defect spectra in phononic crystals
Abstract
Defect modes localize vibrations within phononic-crystal bandgaps. Prescribing their frequencies alone does not ensure separation from competing modes. We use frequency-dependent selection weights to combine attraction of target-adjacent modes with repulsion of competing in-gap modes. Only the central defect cell is optimized within a previously designed, fixed host bandgap. Cell-level Craig--Bampton reduction retains physical interface coordinates, allowing the host contribution to be assembled once while the defect basis and matrices are updated. Across three numerical cases, the reduced-order method accelerates defect optimization by approximately 13--20 times. A comparison with attraction-only optimization shows that the combined objective moves competing modes away from the target and increases the minimum target-to-non-target frequency separation. Full-order reanalysis shows that the optimized modes remain close to the prescribed frequencies and localized around the defect. A finite-array calculation shows enhanced response near the target relative to the defect-free host under the prescribed loading.
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BibTeX
@misc{xu2026reducedorder,
title = {{Reduced-order topology optimization of defect spectra in phononic crystals}},
author = {Xinlin Xu and Junji Kato},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.26435},
eprint = {2605.26435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.26435},
}
RIS
TY - UNPB
TI - Reduced-order topology optimization of defect spectra in phononic crystals
AU - Xinlin Xu
AU - Junji Kato
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2605.26435
UR - https://arxiv.org/abs/2605.26435
AB - Defect modes localize vibrations within phononic-crystal bandgaps. Prescribing their frequencies alone does not ensure separation from competing modes. We use frequency-dependent selection weights to combine attraction of target-adjacent modes with repulsion of competing in-gap modes. Only the central defect cell is optimized within a previously designed, fixed host bandgap. Cell-level Craig--Bampton reduction retains physical interface coordinates, allowing the host contribution to be assembled once while the defect basis and matrices are updated. Across three numerical cases, the reduced-order method accelerates defect optimization by approximately 13--20 times. A comparison with attraction-only optimization shows that the combined objective moves competing modes away from the target and increases the minimum target-to-non-target frequency separation. Full-order reanalysis shows that the optimized modes remain close to the prescribed frequencies and localized around the defect. A finite-array calculation shows enhanced response near the target relative to the defect-free host under the prescribed loading.
ER -