Space-Frequency PGD Formulation with Refined Sinusoidal Kinematics for Forced Vibration Analysis of Composite and Sandwich Beams
M. NDIAYE, P. VIDAL, G. DI CARA, L. GALLIMARD, O. POLIT
Abstract. Composite and sandwich beam structures are widely used in weight-sensitive industrial applications for their high stiffness-to-mass ratio. Their vibrational behavior, however, involves through-thickness effects that classical beam theories capture poorly, while full three-dimensional finite element analyses remain computationally expensive when repeated frequency sweeps are required. A reduced-order strategy is presented, combining a refined sinus kinematics (SinRef-7p) with a Proper Generalized Decomposition (PGD) separating the displacement field between the two-dimensional cross-section domain and the load frequency. The resulting nonlinear problem is solved through a greedy enrichment algorithm, whose robustness is further enhanced by a simultaneous update of all frequency functions once the spatial basis is complete. This step is shown to be essential when, even in the presence of a corrective pair, an accurate prediction of the frequency response cannot be fully restored. It then enables further correction of the solution until convergence is achieved. The approach is validated on symmetric, antisymmetric and sandwich laminated beams for slenderness ratios from 2 to 20, showing that the PGD reduction preserves the accuracy of the underlying SinRef-7p model.
Keywords
Composite, Sandwich, Beam, Proper Generalized Decomposition, Space-Frequency Separation, Refined Sinus Model, Frequency Response Function
Published online 11/8/2026, 6 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: M. NDIAYE, P. VIDAL, G. DI CARA, L. GALLIMARD, O. POLIT, Space-Frequency PGD Formulation with Refined Sinusoidal Kinematics for Forced Vibration Analysis of Composite and Sandwich Beams, Materials Research Proceedings, Vol. 73, pp 118-123, 2026
DOI: https://doi.org/10.21741/9781644904459-24
The article was published as article 24 of the book Mechanics of Advanced Materials and Structures
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
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