Minimum-weight frames under subresonant harmonic excitation: Robust constraints on dynamic compliance, peak input power, and eigenfrequencies

TL;DR

This paper develops a robust optimization framework for minimum-weight undamped Euler-Bernoulli frames under subresonant harmonic excitation, unifying compliance and power constraints with eigenfrequency analysis, and demonstrates its effectiveness through theoretical and experimental validation.

Contribution

It introduces a semidefinite reformulation for robust dynamic compliance and peak power, enabling certified bounds and optimal designs for complex frame structures.

Findings

Exact eigenvalue reformulation for response measures

Global optimal solution for 10-segment frame

High-quality local solutions for 35-segment frame

Abstract

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.