smallest handheld electronic devices and from the most advanced scientific and
medical equipment to the simplest household items. This monograph is one of the
first on the mechanical engineering market because the authors analyse vibrations
of nanostructures based on various theories of elasticity of the higher order
including the modified coupled stress theory, surface theory, nonlocal theory,
gradient theory and their modifications.
The bulk of the literature on nano-objects is devoted to research in nanomechanics, nanocomposites, the theory of dislocation mechanics, etc. The issues of
strength, durability and time-dependent deterioration of mechanical properties,
which are the main problems for design engineers, are considered. However,
majority of the dynamical problems reported in the available literature are presented
for strongly order reduced systems, i.e. for the governing equations of one degree of
freedom systems of the Duffing type. Moreover, there are no books on nonlinear
dynamics, in particular, chaotic dynamics, for nanomechanical structures in which
systems with an infinite number of degrees of freedom are studied. The issues of the
“truth of chaos” are not analysed, and the scenarios of the transition from periodic
to chaotic vibrations exhibited by nanomechanical systems are not satisfactorily
investigated. There are also very few studies regarding dynamics of nanomechanical structures based on wavelet analysis and analysis of the largest Lyapunov
exponents, while there are practically no results supported by consideration of a
spectrum of Lyapunov exponents. The literature state of the art shows that there are
no works devoted to the study of nanoeffects and the effect of temperature action,
which play a crucial role in obtaining a reliable picture of nanostructural nonlinear
dynamical systems embedded into temperature fields.
The book offers a rigorous mathematical approach and verifies numerous
theory-based modelling of structural members with an emphasis on microelectromechanical structures (MEMS) and nanoelectromechanical structures (NEMS),
whose nonlinear dynamics plays an important role in current research observed in
applied physics and engineering.
There are no competing publications on the market for the book (except perhaps
the two already mentioned), and therefore the book may have a significant impact
on both theoretical- and application-oriented researchers interested in nonlinear
features of nanostructural members.
The authors of this monograph are intended to fill gaps in the above-mentioned
problems.
We would like to acknowledge that a part of the book material has been already
published in the form of papers. We have obtained permission to reuse the mentioned material in our book.
In the case of the papers: J. Awrejcewicz, A. V. Krysko, N. P. Erofeev,
V. Dobriyan, M. A. Barulina, V. A. Krysko, “Quantyfying chaos by various
computational methods. Part 1: Simple systems”, Entropy, 20(3), 2018, 175 and
J. Awrejcewicz, A. V. Krysko, N. P. Erofeev, V. Dobriyan, M. A. Barulina,
V. A. Krysko, “Quantyfying chaos by various computational methods. Part 2:
Vibrations of the Bernoulli-Euler beam subjected to periodic and colored noise”,
vi
Preface
medical equipment to the simplest household items. This monograph is one of the
first on the mechanical engineering market because the authors analyse vibrations
of nanostructures based on various theories of elasticity of the higher order
including the modified coupled stress theory, surface theory, nonlocal theory,
gradient theory and their modifications.
The bulk of the literature on nano-objects is devoted to research in nanomechanics, nanocomposites, the theory of dislocation mechanics, etc. The issues of
strength, durability and time-dependent deterioration of mechanical properties,
which are the main problems for design engineers, are considered. However,
majority of the dynamical problems reported in the available literature are presented
for strongly order reduced systems, i.e. for the governing equations of one degree of
freedom systems of the Duffing type. Moreover, there are no books on nonlinear
dynamics, in particular, chaotic dynamics, for nanomechanical structures in which
systems with an infinite number of degrees of freedom are studied. The issues of the
“truth of chaos” are not analysed, and the scenarios of the transition from periodic
to chaotic vibrations exhibited by nanomechanical systems are not satisfactorily
investigated. There are also very few studies regarding dynamics of nanomechanical structures based on wavelet analysis and analysis of the largest Lyapunov
exponents, while there are practically no results supported by consideration of a
spectrum of Lyapunov exponents. The literature state of the art shows that there are
no works devoted to the study of nanoeffects and the effect of temperature action,
which play a crucial role in obtaining a reliable picture of nanostructural nonlinear
dynamical systems embedded into temperature fields.
The book offers a rigorous mathematical approach and verifies numerous
theory-based modelling of structural members with an emphasis on microelectromechanical structures (MEMS) and nanoelectromechanical structures (NEMS),
whose nonlinear dynamics plays an important role in current research observed in
applied physics and engineering.
There are no competing publications on the market for the book (except perhaps
the two already mentioned), and therefore the book may have a significant impact
on both theoretical- and application-oriented researchers interested in nonlinear
features of nanostructural members.
The authors of this monograph are intended to fill gaps in the above-mentioned
problems.
We would like to acknowledge that a part of the book material has been already
published in the form of papers. We have obtained permission to reuse the mentioned material in our book.
In the case of the papers: J. Awrejcewicz, A. V. Krysko, N. P. Erofeev,
V. Dobriyan, M. A. Barulina, V. A. Krysko, “Quantyfying chaos by various
computational methods. Part 1: Simple systems”, Entropy, 20(3), 2018, 175 and
J. Awrejcewicz, A. V. Krysko, N. P. Erofeev, V. Dobriyan, M. A. Barulina,
V. A. Krysko, “Quantyfying chaos by various computational methods. Part 2:
Vibrations of the Bernoulli-Euler beam subjected to periodic and colored noise”,
vi
Preface