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Autores principales: Tyburec, Marek, Handa, Marouan, Havelka, Jan, Zeman, Jan
Formato: Preprint
Publicado: 2026
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Acceso en línea:https://arxiv.org/abs/2603.00012
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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
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institution arXiv
publishDate 2026
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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