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Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields
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.
Chaos in Structural Mechanics
This volume introduces new approaches to modeling strongly nonlinear behaviour of structural mechanical units: beams, plates and shells or composite systems. The text draws on bifurcation theory and chaos, emphasizing control and stability of objects and systems.
Thermo-Dynamics of Plates and Shells
This monograph is devoted to nonlinear dynamics of thin plates and shells with thermosensitive excitation. Because of the variety of sizes and types of mathematical models in current use, there is no prospect of solving them analytically. However, the book emphasizes a rigorous mathematical treatment of the obtained differential equations, since it helps efficiently in further developing of various suitable numerical algorithms to solve the stated problems.
Entropy in Dynamic Systems
In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.
Deterministic Chaos In One Dimensional Continuous Systems
This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations.Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling,...
Introduction to Asymptotic Methods
Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m
Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells
From the reviews: "A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." Journal of Sound and Vibration
Mathematical Models of Higher Orders
This book offers a valuable methodological approach to the state-of-the-art of the classical plate/shell mathematical models, exemplifying the vast range of mathematical models of nonlinear dynamics and statics of continuous mechanical structural members. The main objective highlights the need for further study of the classical problem of shell dynamics consisting of mathematical modeling, derivation of nonlinear PDEs, and of finding their solutions based on the development of new and effective numerical techniques. The book is designed for a broad readership of graduate students in mechanical and civil engineering, applied mathematics, and physics, as well as to researchers and professionals interested in a rigorous and comprehensive study of modeling non-linear phenomena governed by PDEs.
Mesh Methods for Boundary-Value Problems and Applications
This book gathers papers presented at the 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, which was held in Kazan, Russia, in October 2020. The papers address the following topics: the theory of mesh methods for boundary-value problems in mathematical physics; non-linear mathematical models in mechanics and physics; algorithms for solving variational inequalities; computing science; and educational systems. Given its scope, the book is chiefly intended for students in the fields of mathematical modeling science and engineering. However, it will also benefit scientists and graduate students interested in these fields.
Elastic and Thermoelastic Problems in Nonlinear Dynamics of Structural Members
From the reviews: "A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." Journal of Sound and Vibration
