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Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields

Regular and Chaotic Dynamics of Micro/Nano Beams, and Cylindrical Panels

  • Focus on nonlinear (chaotic) dynamics of mass distributed-parameter nanomechanical structures
  • Pedagogical style
  • Overview of nanoshells, nanoplates and nanobeams
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advanced Structured Materials (STRUCTMAT, volume 142)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxi
  2. Nanostructural Members in Various Fields: A Literature Review

    • Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko
    Pages 1-23
  3. Size-Dependent Theories of Beams, Plates and Shells

    • Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko
    Pages 25-78
  4. Lyapunov Exponents and Methods of Their Analysis

    • Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko
    Pages 79-91
  5. Reliability of Chaotic Vibrations of Euler-Bernoulli Beams with Clearance

    • Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko
    Pages 93-112
  6. Analysis of Simple Nonlinear Dynamical Systems

    • Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko
    Pages 113-129
  7. Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field

    • Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko
    Pages 131-195
  8. Mathematical Models of Functionally Graded Beams in Temperature Field

    • Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko
    Pages 197-294
  9. Thermoelastic Vibrations of Timoshenko Microbeams (Modified Couple Stress Theory)

    • Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko
    Pages 295-332
  10. Vibrations of Size-Dependent Beams Under Topologic Optimization and Temperature Field

    • Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko
    Pages 333-402

About this book

This book is devoted to researchers and teachers, as well as graduate students, undergraduates and bachelors in engineering mechanics, nano-mechanics, nanomaterials, nanostructures and applied mathematics. It presents a collection of the latest developments in the field of nonlinear (chaotic) dynamics of mass distributed-parameter nanomechanical structures, providing a rigorous and comprehensive study of modeling nonlinear phenomena. It is written in a unique pedagogical style particularly suitable for independent study and self-education. In addition, the book achieves a good balance between Western and Eastern extensive studies of the mathematical problems of nonlinear vibrations of structural members.


Authors and Affiliations

  • Department of Automation, Biomechanics & Mechatronics, Lodz University of Technology, Lodz, Poland

    Jan Awrejcewicz

  • Applied Mathematics and Systems Analysis, Saratov State Technical University, Saratov, Russia

    Anton V. Krysko

  • Department of Mathematics and Modeling, Saratov State Technical University, Saratov, Russia

    Maxim V. Zhigalov, Vadim A. Krysko

About the authors

Anton Krysko (A.V. Krysko) obtained his Ph.D. degree in Mechanics of Solids from the Department of Strength of Materials, Saratov State Technical University in 1995, D.Sci. degree in Mechanics of Solids 2003 and a habilitation from Saratov State Technical University in 2008. He has worked as a professor at the Department of Applied Mathematics and Theory Navigation Device as well as Head of the Department of Higher Mathematics and Mechanics. Currently he is a professor at the Department of Applied Mathematics and System Analysis. His research interests cover advanced numerical methods for MEMS / NEMS sensors, EEG signal processing, nonlinear dynamics and chaotic vibrations continues mechanical systems as well as nano-structures, thermoelasticity and thermoplasticity, the theory of optimization of mechanical systems. For his scientific merits, he received prestigious national awards and distinctions, among them the Diploma of the Ministry of Education and Science of the Russian Federation for the great and fruitful work on the preparation of the teaching staff; development of scientific research on topical issues of fundamental and applied science, 2011, Moscow, Russia


Vadim Krysko (V. A. Krysko) obtained his Ph.D. degree in Mechanics of Solids from the Department of Structural mechanics Saratov State Technical University, USSR in 1967, and D.Sci. degree in Mechanics of Solids from Moscow State University of Civil Engineering in 1978. In 1982 he became a full professor, the academic rank of professor obtained from the Department of Higher Mathematics, Saratov State Technical University. In 2008 he founded the Department of Mathematics and Modeling, that he still manages. His research interest are on thermoelasticity and thermoplasticity, the theory of optimization of mechanical systems, the theory of propagation of elastic waves upon impact, the theory of coupled problems of thermoelasticity and the interaction of flexible elastic shellswith a transonic gas flow, numerical methods for solving nonlinear problems of shells theory, nonlinear dynamics and chaos in MEMS / NEMS resonators, nonlinear dynamics of nano structures as well as signal processing for brain-computer interfaces (BCI) and EEG signal processing. For his scientific achievements, he received prestigious awards and distinctions, including the title of Honored Personality of science and technology of the Russian Federation  for special merits in the field of science and technology (1987), and titles of Doctor Honoris Causa of the Lodz University of Technology, Poland (2012). Vadim Krysko opened and developed novel scientific directions for research in the construction, justification and numerical implementation of new classes of equations of mathematical physics of hyperbolic-parabolic types and proposed effective methods for their numerical solution. 


Jan Awrejcewicz obtained his PhD in technical sciences and a postdoctoral degree (habilitation) at the Mechanical Faculty of the Lodz University of Technology. In 1994, he received the title of Professor from the President of Poland. In 1998 he founded the Department of Automation, Biomechanics and Mechatronics, that he is still managing. Since 2013 he has been a member of the Polish Central Commission for Degrees and Titles, and since 2019 also of the Council for Scientific Excellence. His scientific achievements cover asymptotic methods for continuous and discrete mechanical systems considering thermoelasticity and tribology, and computer implementations using symbolic calculus, nonlinear dynamics of mechanical systems with friction and impacts, as well as engineering biomechanics. For his scientific merits he received numerous prestigious awards and distinctions, among them the Humboldt Award (twice) and  titles of the Honorary Doctor of CzÄ™stochowa University of Technology (2013), University of Technology and Humanities in Bielsko-BiaÅ‚a (2013),Kielce University of Technology (2019), National Technical University "Kharkiv Polytechnic Institute" (2019), and GdaÅ„sk University of Technology (2019).


Zhigalov M.V. has a Doctor of Physics and Mathematics from Saratov State Technical University. His scientific achievements cover topics as Nonlinear (chaotic) dynamics of mechanical systems, contact problems of beams and plates nonlinear dynamics, wavelet analysis in studies of the nonlinear dynamics of mechanical systems, historical processes, and brain signals, topological optimization of thermoelastic bodies, construction of methods for lowering the order, dimension, and linearization for nonlinear partial differential equations of high order.

Bibliographic Information

  • Book Title: Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields

  • Book Subtitle: Regular and Chaotic Dynamics of Micro/Nano Beams, and Cylindrical Panels

  • Authors: Jan Awrejcewicz, Anton V. Krysko, Maxim V. Zhigalov, Vadim A. Krysko

  • Series Title: Advanced Structured Materials

  • DOI: https://doi.org/10.1007/978-3-030-55993-9

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-55992-2Published: 09 October 2020

  • Softcover ISBN: 978-3-030-55995-3Published: 10 October 2021

  • eBook ISBN: 978-3-030-55993-9Published: 08 October 2020

  • Series ISSN: 1869-8433

  • Series E-ISSN: 1869-8441

  • Edition Number: 1

  • Number of Pages: XXI, 402

  • Number of Illustrations: 7 b/w illustrations, 139 illustrations in colour

  • Topics: Mechanical Engineering, Materials Science, general

Buy it now

Buying options

eBook USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access