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M.J. Bader
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Structural Dynamics of Crumpled Thin Sheets
Beyond Wrinkling: A Numerical and Experimental Study
Master thesis
(2026)
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M.J. Bader, J.L. Herder, Jieun Yang, H. van Beek, G. Radaelli, P.C.J. Hoogenboom
This thesis investigates crumpled thin-sheet bellows as a more compliant alternative to traditional corrugated bellows in vibrationally isolated mechatronic systems (ASML lithography machines). While conventional bellows rely on carefully engineered corrugations, the crumpled foil bellows studied here achieve compliance through an irregular, crumpled morphology, making their dynamic stiffness and vibrational transmissibility difficult to predict. The first part of the thesis is a stand-alone literature review into the diverse approaches employed to model wrinkled and crumpled thin sheets, with their structural dynamics of particular interest. The second part presents original research in which realistic crumpled bellow geometries are generated using explicit non-linear simulations via the dynamic relaxation method, and subsequently dynamically analysed using Hintz–Herting modal reduction. In this way, the static and frequency-dependent emergent stiffness can be extracted and examined as functions of compaction ratio and foil thickness. Experimental measurements of dynamic stiffness are used to validate the numerical trends and to identify the limitations of linearised models for these systems.
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This thesis investigates crumpled thin-sheet bellows as a more compliant alternative to traditional corrugated bellows in vibrationally isolated mechatronic systems (ASML lithography machines). While conventional bellows rely on carefully engineered corrugations, the crumpled foil bellows studied here achieve compliance through an irregular, crumpled morphology, making their dynamic stiffness and vibrational transmissibility difficult to predict. The first part of the thesis is a stand-alone literature review into the diverse approaches employed to model wrinkled and crumpled thin sheets, with their structural dynamics of particular interest. The second part presents original research in which realistic crumpled bellow geometries are generated using explicit non-linear simulations via the dynamic relaxation method, and subsequently dynamically analysed using Hintz–Herting modal reduction. In this way, the static and frequency-dependent emergent stiffness can be extracted and examined as functions of compaction ratio and foil thickness. Experimental measurements of dynamic stiffness are used to validate the numerical trends and to identify the limitations of linearised models for these systems.