A Parametrically Excited Nonlinear Wave Equation
When considering nonlinear waves with periodic parametric forcing the geometry of the spatial domain plays a crucial part. If the spatial domain is a square we find an infinite number of 1 : 1 resonances and in addition accidental resonances. Using Galerk
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Andrei K. Abramian Igor V. Andrianov Valery A. Gaiko Editors
Nonlinear Dynamics of Discrete and Continuous Systems
Advanced Structured Materials Volume 139
Series Editors Andreas Öchsner, Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen, Germany Lucas F. M. da Silva, Department of Mechanical Engineering, Faculty of Engineering, University of Porto, Porto, Portugal Holm Altenbach , Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany
Common engineering materials reach in many applications their limits and new developments are required to fulfil increasing demands on engineering materials. The performance of materials can be increased by combining different materials to achieve better properties than a single constituent or by shaping the material or constituents in a specific structure. The interaction between material and structure may arise on different length scales, such as micro-, meso- or macroscale, and offers possible applications in quite diverse fields. This book series addresses the fundamental relationship between materials and their structure on the overall properties (e.g. mechanical, thermal, chemical or magnetic etc.) and applications. The topics of Advanced Structured Materials include but are not limited to • classical fibre-reinforced composites (e.g. glass, carbon or Aramid reinforced plastics) • metal matrix composites (MMCs) • micro porous composites • micro channel materials • multilayered materials • cellular materials (e.g., metallic or polymer foams, sponges, hollow sphere structures) • porous materials • truss structures • nanocomposite materials • biomaterials • nanoporous metals • concrete • coated materials • smart materials Advanced Structured Materials is indexed in Google Scholar and Scopus.
More information about this series at http://www.springer.com/series/8611
Andrei K. Abramian Igor V. Andrianov Valery A. Gaiko •
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Editors
Nonlinear Dynamics of Discrete and Continuous Systems
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Editors Andrei K. Abramian Institute of Problems in Mechanical Engineering Russian Academy of Sciences St. Petersburg, Russia
Igor V. Andrianov Institute of General Mechanics RWTH Aachen University Aachen, Nordrhein-Westfalen, Germany
Valery A. Gaiko United Institute of Informatics Problems National Academy of Sciences of Belarus Minsk, Belarus
ISSN 1869-8433 ISSN 1869-8441 (electronic) Advanced Structured Materials ISBN 978-3-030-53005-1 ISBN 978-3-030-53006-8 (eBook) https://doi.org/10.1007/978-3-030-53006-8 © Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter devel
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