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.

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

Autorentext

From the beginning of his academic career Jan Awrejcewicz has been associated with the Mechanical Faculty of the Lodz University of Technology, where he obtained a master's degree in engineering, a PhD in technical sciences and a postdoctoral degree (habilitatioin). 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. He is also an Editor-in-Chief of 3 international journals and member of the Editorial Boards of 90 international journals (23 with IF) as well as editor of 25 books and 28 journal special issues. He also reviewed 45 monographs and textbooks and over 600 journal papers for about of 140 journals. His scientific achievements cover issues related to asymptotic methods for continuous and discrete mechanical systems, taking into account thermoelasticity and tribology, and computer implementations using symbolic calculus, nonlinear dynamics of mechanical systems with friction and impacts, as well as engineering biomechanics. He authored/co-authored over 780 journal papers and refereed international conference papers and 50 monographs. For his scientific merits he recived numerous prestigious awards and distinctions, among them titles of the Honoratry Doctor of Cz stochowa University of Technology (2013), University of Technology and Humanities in Bielsko-Biäa (2013), Kielce University of Technology (2019), National Technical University "Kharkiv Polytechnic Institute" (2019), and Gdäsk University of Technology (2019). Vadim Krysko was born in Kiev, Ukraine, on September 21, 1937. He received a master's degree in Civil Engineering from the Saratov State Technical University in 1962. A Ph.D. degree in Mechanics of Solids he obtained from the Saratov State Technical University, USSR in 1967, and D.Sci. degree in Mechanics of Solids he obtained from Moscow Civil Engineering University 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. He is author/co-author of 329 publications in scientific journals and conference proceedings, 8 monographs in English, 8 monographs in Polish, and 16 monographs in Russian. Topics of his research cover such branches of mechanics as 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 shells with a transonic gas flow, numerical methods for solving nonlinear problems of shells theory. Vadim Krysko was a promoter of 58 PhD (postgraduate student) theses. He is currently the Head of the Department of Mathematicsand Modeling, Saratov State Technical University, Russia. In 2012 he was honored by a title of Doctor Honoris Causa of the Lodz University of Technology, Poland. 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.

Inhalt
Nano-Structural Members in Various Fields, Literature Review.- Size-Dependent Theories of Beams, Plates and Shells.- Lyapunov Exponents and Methods of Their Analysis.- Reliability of Chaotic Vibrations of Euler-Bernoulli Beams withClearance.- Analysis of Simple Nonlinear Dynamical Systems.- Mathematical Models of Micro- and Nano-Cylindrical Panels inTemperature Field.- Mathematical Models of Functionally Graded Beams in Temperature Field.- Thermoelastic Vibrations of Timoshenko Microbeams (Modified Couple Stress Theory).- Vibrations of Size-Dependent Beams Under Topologic Optimization and Temperature Field.