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In this work, the systematic validation of a deterministic finite element (FE) model updating procedure for damage assessment is presented using a self-developed modular laboratory experiment. A fundamental, systematic validation of damage assessment methods is rarely conducted and in many experimental investigations, only one type of defect is introduced at only one position. Often, the damage inserted is irreversible and inspections are only performed visually. Thus, the damage introduced and, with it, the results of the damage assessment method considered are often not entirely analyzed in terms of quantity and quality. To address this shortcoming, a modular steel cantilever beam is designed with nine reversible damage positions and the option to insert different damage scenarios in a controlled manner. The measurement data are made available in open-access form which enables a systematic experimental validation of damage assessment methods. To demonstrate such a systematic validation using the modular laboratory experiment, a deterministic FE model updating procedure previously introduced by the authors is applied and extended. The FE model updating approach uses different parameterized damage distribution functions to update the stiffness properties of the structure considered. The mathematical formulation allows for an updating procedure that is independent of the FE mesh resolution and free of assumptions about the defect location while only needing few design variables. In this work, the FE model updating procedure is based only on eigenfrequency deviations. The results show a precise localization within $$\pm \, {0.05}{\textrm{m}}$$ ± 0.05 m of the nine different damage positions and a correct relative quantification of the three different damage scenarios considered. With that, first, it is shown that the deterministic FE model updating procedure presented is suitable for precise damage assessment. Second, this work demonstrates that the opportunity to introduce several reversible damage positions and distinctly defined types and severities of damage into the laboratory experiment presented generally enables the systematic experimental validation of damage assessment methods.

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Bistable unsymmetrical laminates have received significant attention in morphing applications due to their ability to attain multiple shapes when subjected to thermal loads. Morphing structures in general are subjected to dynamic operating conditions. Also, the highly nonlinear snap-through transition between stable configurations possesses rich dynamic characteristics. Therefore, understanding the dynamic characteristics of bistable laminates is essential for designing morphing structures constituting bistable elements. Thus, the present study aims to explore the dynamics of bistable unsymmetrical laminates by evaluating their natural vibration characteristics associated with small-amplitude dynamic excitation around the static equilibrium configurations. A refined semi-analytical framework is proposed to analyze the natural vibration characteristics of the bistable laminate, where the potential energy is expressed only in terms of the unknown coefficients of the assumed out-of-plane displacement function. The in-plane components are separately evaluated using the in-plane equilibrium equations and compatibility conditions. In the dynamic analysis, perturbations are imposed on the static equilibrium configurations to capture the modal characteristics. A full geometrically nonlinear finite element (FE) model of the bistable laminate has been created in a commercially available FE package to compare semi-analytical solutions. To validate the proposed frameworks, an experimental strategy to capture the natural frequencies of a bistable laminate is presented in this paper. Unsymmetric laminates mounted at its center have been used for the experimental testing, where the vibrations are measured using miniature integrated electronics piezoelectric accelerometer sensors attached at the corners. The semi-analytical and FE results are validated against the experimental observations for the selected unsymmetrical cross-ply laminates. The proposed frameworks are further extended to a family of unsymmetrical variable-stiffness (VS) laminates generated using curvilinear fiber alignments. The selected VS family can generate bistable shapes without any twisting curvature similar to that of an unsymmetrical cross-ply laminate, where the designer can expand the design space with a plethora of multiple configurations. A parametric study is performed by tailoring the VS parameters to investigate the influence of curvilinear fiber alignments on the natural vibration characteristics of bistable VS laminates.