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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.00012 |
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| _version_ | 1866908856705089536 |
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| author | Tyburec, Marek Handa, Marouan Havelka, Jan Zeman, Jan |
| author_facet | Tyburec, Marek Handa, Marouan Havelka, Jan Zeman, Jan |
| contents | This work addresses minimum-weight design of undamped Euler-Bernoulli frame structures under subresonant single-frequency harmonic excitations, focusing on (robust) dynamic compliance and (robust) peak input power with ellipsoidal load uncertainty. We develop a semidefinite reformulation of robust dynamic compliance for subresonant single-frequency excitation and prove its equivalence to robust peak input power. We show that both these response measures admit an exact reformulation as a free-vibration eigenvalue constraint with design-independent mass augmentation, unifying static, dynamic, and modal requirements. Despite the nonconvex polynomial dependence on cross-sectional areas, certified bounds on global minimizers are obtained via the moment-sum-of-squares hierarchy of semidefinite relaxations. Benchmark studies on 10- and 35-segment frames corroborate the theory. For the 10-segment problem, we obtain the global optimum; for the 35-segment frame, we find high-quality locally-optimal designs that substantially improve on the best known one. We further fabricate and experimentally validate an additional design that closely matches the predictions of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00012 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimum-weight frames under subresonant harmonic excitation: Robust constraints on dynamic compliance, peak input power, and eigenfrequencies Tyburec, Marek Handa, Marouan Havelka, Jan Zeman, Jan Optimization and Control This work addresses minimum-weight design of undamped Euler-Bernoulli frame structures under subresonant single-frequency harmonic excitations, focusing on (robust) dynamic compliance and (robust) peak input power with ellipsoidal load uncertainty. We develop a semidefinite reformulation of robust dynamic compliance for subresonant single-frequency excitation and prove its equivalence to robust peak input power. We show that both these response measures admit an exact reformulation as a free-vibration eigenvalue constraint with design-independent mass augmentation, unifying static, dynamic, and modal requirements. Despite the nonconvex polynomial dependence on cross-sectional areas, certified bounds on global minimizers are obtained via the moment-sum-of-squares hierarchy of semidefinite relaxations. Benchmark studies on 10- and 35-segment frames corroborate the theory. For the 10-segment problem, we obtain the global optimum; for the 35-segment frame, we find high-quality locally-optimal designs that substantially improve on the best known one. We further fabricate and experimentally validate an additional design that closely matches the predictions of the model. |
| title | Minimum-weight frames under subresonant harmonic excitation: Robust constraints on dynamic compliance, peak input power, and eigenfrequencies |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.00012 |