Damping by branching: a bioinspiration from trees

Man-made slender structures are known to be sensitive to high levels of vibration, due to their flexibility, which often cause irreversible damage. In nature, trees repeatedly endure large amplitudes of motion, mostly caused by strong climatic events, yet with minor or no damage in most cases. A new damping mechanism inspired by the architecture of trees is here identified and characterized in the simplest tree-like structure, a Y-shape branched structure. Through analytical and numerical analyses of a simple two-degree-of-freedom model, branching is shown to be the key ingredient in this protective mechanism that we call damping-by-branching. It originates in the geometrical nonlinearities so that it is specifically efficient to damp out large amplitudes of motion. A more realistic model, using flexible beam approximation, shows that the mechanism is robust. Finally, two bioinspired architectures are analyzed, showing significant levels of damping achieved via branching with typically 30% of the energy being dissipated in one oscillation. This concept of damping-by-branching is of simple practical use in the design of slender flexible structures.Comment: 10 pages, 10 figure

Amortissement par le branchement des structures flexibles : une approche bio-inspirée des arbres

Extreme dynamical loads are a cause of damage of man-made structures. In nature, some plants, trees in particular, repeatedly endure extreme loads mostly caused by strong climatic events. For such living structures, it is of vital importance to efficiently dissipate mechanical energy received by such loading conditions and evolution may well have optimized their damping mechanism. The bio-inspired idea defended here is that structural branching of flexible structures brings a robust and specific damping mechanism for vibrations of large amplitude. The large amplitude dynamics of an elementary branched model with two degrees of freedom is studied, showing a non-linear energy transfer between normal modes. This transfer originates in the geometrical nonlinearities, explained by the centrifugal forces acting on branches when the trunk oscillates. The transfer is effective when the frequency ratio of the corresponding normal modes is approximately 2. This mechanism, coined \mbox{"damping by branching"}, is specifically efficient to dampen large amplitude vibrations. It appears as robust against the variety of possible sources of dissipation of the structure, including the interaction with a surrounding fluid. Using the finite element method and a flexible beam approximation, the dynamics of a continuous branched model, excited by pull-and-released or by harmonic forcing, is analysed and demonstrates the applicability of the mechanism to more complex structures. This damping mechanism is experimentally displayed on a flexible branched structure of which modal frequencies have been tuned. These results lead to the design of a branched dynamic absorber for rotating systems, which offers better performances than those of a conventional and equivalent dynamical absorber in a certain range of amplitudes. Finally, the analysis of a multiple-branched model suggests that this mechanism is actually present in trees.Les chargements dynamiques extrêmes sont une cause importante des dommages des structures. Dans la nature, certaines plantes, particulièrement les arbres, résistent régulièrement à des chargements extrêmes comme lors de tempêtes. Pour ces structures vivantes, produits de l'évolution, dissiper efficacement l'énergie mécanique reçue lors de tels chargements conditionne leur survie et le mécanisme de leur amortissement est donc probablement optimisé. L'idée bio-inspirée défendue ici est que le branchement offre aux structures flexibles un mécanisme d'amortissement robuste et spécifique aux vibrations de grande amplitude. La dynamique en grands déplacements d'un modèle branché élémentaire ayant deux degrés de liberté est étudiée, mettant en évidence un transfert non linéaire d'énergie entre les modes propres. Ce transfert provient de non-linéarités géométriques et s'explique par une excitation centrifuge des branches par l'oscillation du tronc ; cette excitation est effective lorsque le rapport des fréquences des modes correspondants est approximativement de 2. Ce mécanisme, dénommé \mbox{"amortissement par le branchement"}, produit une dissipation spécifique qui augmente avec l'amplitude des vibrations. Il apparaît comme robuste vis-à-vis de la variété des sources possibles de dissipation de la structure, provenant, par exemple, de l'interaction avec un fluide environnant. En utilisant la méthode des éléments finis, l'analyse de la dynamique en grands déplacements d'un modèle branché continu constitué de poutres, excité par lâcher ou par forçage, montre l'applicabilité du mécanisme à des structures plus complexes. Une expérience met en évidence ce mécanisme d'amortissement par le branchement sur une structure flexible branchée et réglée en fréquence. Ces résultats ont permis de concevoir un absorbeur dynamique branché pour les systèmes en rotation, lequel offre des performances supérieures, dans une certaine gamme d'amplitudes, à celles d'un absorbeur dynamique classique équivalent. Enfin, l'analyse d'un modèle ramifié suggère que ce mécanisme est effectivement présent dans les arbres

Oscillation damping in trees

International audienceOscillation damping is of vital importance for trees to withstand strong gusty winds. Tree adaptation to wind loading takes place over a long time and during a storm only passive damping mechanisms can reduce the impact of the wind on trunk and roots. Structural damping, a phenomenon, which is associated with the conspicuous movements of the branches relative to the trunk is of particular importance. Primary and higher order branches can be seen as multiple tuned mass dampers. Moreover, as the frequency bands overlap within branches and between primary branches and the entire tree, resonance energy transfer can distribute mechanical energy over the entire tree, such that it is dissipated more effectively than in a tree with stiff branches and not so much focused on the tree trunk and the roots. Theoretical studies using modal analysis and finite element methods have supported these assertions. Next to "multiple mass damping" and "multiple resonance damping", both characterized by linear coupling between the elements, a third non linear mode, operative at large amplitudes has been identified: "damping by branching". In all these not mutually exclusive concepts frequency tuning between the elements appears to be a fundamental requisite. (C) 2013 Elsevier Ireland Ltd. All rights reserved

Amortissement par le branchement des structures flexibles (une approche bio-inspirée des arbres)

Les chargements dynamiques extrêmes sont une cause importante des dommages des structures. Dans la nature, certaines plantes, particulièrement les arbres, résistent régulièrement à des chargements extrêmes comme lors de tempêtes. Pour ces structures vivantes, produits de l'évolution, dissiper efficacement l'énergie mécanique reçue lors de tels chargements conditionne leur survie et le mécanisme de leur amortissement est donc probablement optimisé. L'idée bio-inspirée défendue ici est que le branchement offre aux structures flexibles un mécanisme d'amortissement robuste et spécifique aux vibrations de grande amplitude. La dynamique en grands déplacements d'un modèle branché élémentaire ayant deux degrés de liberté est étudiée, mettant en évidence un transfert non linéaire d'énergie entre les modes propres. Ce transfert provient de non-linéarités géométriques et s'explique par une excitation centrifuge des branches par l'oscillation du tronc ; cette excitation est effective lorsque le rapport des fréquences des modes correspondants est approximativement de 2. Ce mécanisme, dénommé \mbox{"amortissement par le branchement"}, produit une dissipation spécifique qui augmente avec l'amplitude des vibrations. Il apparaît comme robuste vis-à-vis de la variété des sources possibles de dissipation de la structure, provenant, par exemple, de l'interaction avec un fluide environnant. En utilisant la méthode des éléments finis, l'analyse de la dynamique en grands déplacements d'un modèle branché continu constitué de poutres, excité par lâcher ou par forçage, montre l'applicabilité du mécanisme à des structures plus complexes. Une expérience met en évidence ce mécanisme d'amortissement par le branchement sur une structure flexible branchée et réglée en fréquence. Ces résultats ont permis de concevoir un absorbeur dynamique branché pour les systèmes en rotation, lequel offre des performances supérieures, dans une certaine gamme d'amplitudes, à celles d'un absorbeur dynamique classique équivalent. Enfin, l'analyse d'un modèle ramifié suggère que ce mécanisme est effectivement présent dans les arbresExtreme dynamical loads are a cause of damage of man-made structures. In nature, some plants, trees in particular, repeatedly endure extreme loads mostly caused by strong climatic events. For such living structures, it is of vital importance to efficiently dissipate mechanical energy received by such loading conditions and evolution may well have optimized their damping mechanism. The bio-inspired idea defended here is that structural branching of flexible structures brings a robust and specific damping mechanism for vibrations of large amplitude. The large amplitude dynamics of an elementary branched model with two degrees of freedom is studied, showing a non-linear energy transfer between normal modes. This transfer originates in the geometrical nonlinearities, explained by the centrifugal forces acting on branches when the trunk oscillates. The transfer is effective when the frequency ratio of the corresponding normal modes is approximately 2. This mechanism, coined \mbox{"damping by branching"}, is specifically efficient to dampen large amplitude vibrations. It appears as robust against the variety of possible sources of dissipation of the structure, including the interaction with a surrounding fluid. Using the finite element method and a flexible beam approximation, the dynamics of a continuous branched model, excited by pull-and-released or by harmonic forcing, is analysed and demonstrates the applicability of the mechanism to more complex structures. This damping mechanism is experimentally displayed on a flexible branched structure of which modal frequencies have been tuned. These results lead to the design of a branched dynamic absorber for rotating systems, which offers better performances than those of a conventional and equivalent dynamical absorber in a certain range of amplitudes. Finally, the analysis of a multiple-branched model suggests that this mechanism is actually present in treesPALAISEAU-Polytechnique (914772301) / SudocSudocFranceF