Academic Journal
First return time to the contact hyperplane for n-degree-of-freedom vibro-impact systems
| العنوان: | First return time to the contact hyperplane for n-degree-of-freedom vibro-impact systems |
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| المؤلفون: | Le Thi, Huong, Junca, Stéphane, Legrand, Mathias |
| المساهمون: | Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA), Inria-SIC Sophia Antipolis, Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), COmplex Flows For Energy and Environment (COFFEE), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA), Structural Dynamics and Vibration Laboratory Montréal, Department of Mechanical Engineering Montréal, McGill University = Université McGill Montréal, Canada -McGill University = Université McGill Montréal, Canada |
| المصدر: | ISSN: 1531-3492. |
| بيانات النشر: | HAL CCSD American Institute of Mathematical Sciences |
| سنة النشر: | 2022 |
| المجموعة: | HAL Université Côte d'Azur |
| مصطلحات موضوعية: | non-smooth analysis, grazing, unilateral contact, Poincaré section, First Return Time, MSC 34A38, 70K50, 70H14 (70K75), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MECA.VIBR]Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph] |
| الوصف: | International audience ; The paper deals with the dynamics of conservative $N$-degree-of-freedom vibro-impact systems involving one unilateral contact condition and a linear free flow. Among all possible trajectories, grazing orbits exhibit a contact occurrence with vanishing incoming velocity which generates mathematical difficulties. Such problems are commonly tackled through the definition of a Poincaré section and the attendant First Return Map. It is known that the First Return Time to the Poincaré section features a square-root singularity near grazing. In this work, a non-orthodox yet natural and intrinsic Poincaré section is chosen to revisit the square-root singularity. It is based on the unilateral condition but is not transverse to the grazing orbits. A detailed investigation of the proposed Poincaré section is provided. Higher-order singularities in the First Return Time are exhibited. Also, activation coefficients of the square-root singularity for the First Return Map are defined. For the linear and periodic grazing orbits from which bifurcate nonlinear modes, one of these coefficients is necessarily non-vanishing. The present work is a step towards the stability analysis of grazing orbits, which still stands as an open problem. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| DOI: | 10.3934/dcdsb.2021031 |
| الاتاحة: | https://hal.science/hal-01957546 https://hal.science/hal-01957546v2/document https://hal.science/hal-01957546v2/file/FRT-20-05-10.pdf https://doi.org/10.3934/dcdsb.2021031 |
| Rights: | http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.7F3DCBA8 |
| قاعدة البيانات: | BASE |
| DOI: | 10.3934/dcdsb.2021031 |
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