Geometrical Nonlinearity of Circular Plates and Membranes: an Alternative Method
| Autor: | Xin Zhou, Dylan Cattiaux, Andrew Fefferman, Eddy Collin, Sumit Kumar |
|---|---|
| Přispěvatelé: | Ultra-basses températures (NEEL - UBT), Institut Néel (NEEL), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Nano and Microsystems - IEMN (NAM6 - IEMN), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Ultra-basses températures (UBT) |
| Rok vydání: | 2019 |
| Předmět: |
010302 applied physics
Work (thermodynamics) Condensed Matter - Mesoscale and Nanoscale Physics Generalization Computer science Numerical analysis Mathematical analysis Structure (category theory) General Physics and Astronomy Motion (geometry) FOS: Physical sciences 02 engineering and technology 021001 nanoscience & nanotechnology Mechanics Condensed Matter Physics 01 natural sciences Nano-devices Stress (mechanics) Simple (abstract algebra) Normal mode 0103 physical sciences Mesoscale and Nanoscale Physics (cond-mat.mes-hall) [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat] 0210 nano-technology |
| Zdroj: | Journal of Applied Physics Journal of Applied Physics, 2020, 128 (10), pp.104501. ⟨10.1063/5.0012329⟩ Journal of Applied Physics, American Institute of Physics, 2020, 128 (10), pp.104501. ⟨10.1063/5.0012329⟩ |
| ISSN: | 0021-8979 1089-7550 |
| DOI: | 10.48550/arxiv.1910.02852 |
| Popis: | International audience; We apply the well-established theoretical method developed for geometrical nonlinearities of micro/nano-mechanical clamped beams to circular drums. The calculation is performed under the same hypotheses, the extra difficulty being to analytically describe the (coordinate-dependent) additional stress generated in the structure by the motion. Specifically, the model applies to non-axisymmetric mode shapes. An analytic expression is produced for the Duffing (hardening) nonlinear coefficient, which requires only the knowledge of the mode shape functions to be evaluated. This formulation is simple to handle, and does not rely on complex numerical methods. Moreover, no hypotheses are made on the drive scheme and the nature of the in-plane stress: it is not required to be of electrostatic origin. We confront our predictions with both typical experimental devices and relevant theoretical results from the literature. Generalization of the presented method to Duffing-type mode-coupling should be a straightforward extension of this work. We believe that the presented modeling will contribute to the development of nonlinear physics implemented in 2D micro/nano-mechanical structures. |
| Databáze: | OpenAIRE |
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