The Mechanics Of Nonlinear Systems With Internal Resonances

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The Mechanics Of Nonlinear Systems With Internal Resonances

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Author : Arkadiy I. Manevich
language : en
Publisher: World Scientific
Release Date : 2005

The Mechanics Of Nonlinear Systems With Internal Resonances written by Arkadiy I. Manevich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.

One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.

The Mechanics Of Nonlinear Systems With Internal Resonances

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Author : Arkadiy I. Manevich
language : en
Publisher: World Scientific
Release Date : 2005

The Mechanics Of Nonlinear Systems With Internal Resonances written by Arkadiy I. Manevich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.

One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.

The Mechanics Of Nonlinear Systems With Internal Resonances

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Author : A. I Manevitch
language : en
Publisher:
Release Date : 2005

The Mechanics Of Nonlinear Systems With Internal Resonances written by A. I Manevitch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

Nonlinear Mechanics Of Shells And Plates In Composite Soft And Biological Materials

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Author : Marco Amabili
language : en
Publisher: Cambridge University Press
Release Date : 2018-11

Nonlinear Mechanics Of Shells And Plates In Composite Soft And Biological Materials written by Marco Amabili and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11 with Mathematics categories.

This book guides the reader into the modelling of shell structures in applications where advanced composite materials or complex biological materials must be described with great accuracy. A valuable resource for researchers, professionals and graduate students, it presents a variety of practical concepts, diagrams and numerical results.

Asymptotic Methods In The Theory Of Non Linear Oscillations

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Author : Nikolaĭ Nikolaevich Bogoli︠u︡bov
language : en
Publisher: CRC Press
Release Date : 1961

Asymptotic Methods In The Theory Of Non Linear Oscillations written by Nikolaĭ Nikolaevich Bogoli︠u︡bov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Science categories.

Nonlinear Vibrations And Stability Of Shells And Plates

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Author : Marco Amabili
language : en
Publisher: Cambridge University Press
Release Date : 2008-01-14

Nonlinear Vibrations And Stability Of Shells And Plates written by Marco Amabili and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-14 with Science categories.

This unique book explores both theoretical and experimental aspects of nonlinear vibrations and stability of shells and plates. It is ideal for researchers, professionals, students, and instructors. Expert researchers will find the most recent progresses in nonlinear vibrations and stability of shells and plates, including advanced problems of shells with fluid-structure interaction. Professionals will find many practical concepts, diagrams, and numerical results, useful for the design of shells and plates made of traditional and advanced materials. They will be able to understand complex phenomena such as dynamic instability, bifurcations, and chaos, without needing an extensive mathematical background. Graduate students will find (i) a complete text on nonlinear mechanics of shells and plates, collecting almost all the available theories in a simple form, (ii) an introduction to nonlinear dynamics, and (iii) the state of art on the nonlinear vibrations and stability of shells and plates, including fluid-structure interaction problems.

Nonstationary Resonant Dynamics Of Oscillatory Chains And Nanostructures

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Author : Leonid I. Manevitch
language : en
Publisher: Springer
Release Date : 2017-07-25

Nonstationary Resonant Dynamics Of Oscillatory Chains And Nanostructures written by Leonid I. Manevitch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-25 with Technology & Engineering categories.

This book suggests a new common approach to the study of resonance energy transport based on the recently developed concept of Limiting Phase Trajectories (LPTs), presenting applications of the approach to significant nonlinear problems from different fields of physics and mechanics. In order to highlight the novelty and perspectives of the developed approach, it places the LPT concept in the context of dynamical phenomena related to the energy transfer problems and applies the theory to numerous problems of practical importance. This approach leads to the conclusion that strongly nonstationary resonance processes in nonlinear oscillator arrays and nanostructures are characterized either by maximum possible energy exchange between the clusters of oscillators (coherence domains) or by maximum energy transfer from an external source of energy to the chain. The trajectories corresponding to these processes are referred to as LPTs. The development and the use of the LPTs concept a re motivated by the fact that non-stationary processes in a broad variety of finite-dimensional physical models are beyond the well-known paradigm of nonlinear normal modes (NNMs), which is fully justified either for stationary processes or for nonstationary non-resonance processes described exactly or approximately by the combinations of the non-resonant normal modes. Thus, the role of LPTs in understanding and analyzing of intense resonance energy transfer is similar to the role of NNMs for the stationary processes. The book is a valuable resource for engineers needing to deal effectively with the problems arising in the fields of mechanical and physical applications, when the natural physical model is quite complicated. At the same time, the mathematical analysis means that it is of interest to researchers working on the theory and numerical investigation of nonlinear oscillations.

Geometric Mechanics And Its Applications

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Author : Weipeng Hu
language : en
Publisher: Springer Nature
Release Date : 2023-01-01

Geometric Mechanics And Its Applications written by Weipeng Hu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Technology & Engineering categories.

To make the content of the book more systematic, this book mainly briefs some related basic knowledge reported by other monographs and papers about geometric mechanics. The main content of this book is based on the last 20 years’ jobs of the authors. All physical processes can be formulated as the Hamiltonian form with the energy conservation law as well as the symplectic structure if all dissipative effects are ignored. On the one hand, the important status of the Hamiltonian mechanics is emphasized. On the other hand, a higher requirement is proposed for the numerical analysis on the Hamiltonian system, namely the results of the numerical analysis on the Hamiltonian system should reproduce the geometric properties of which, including the first integral, the symplectic structure as well as the energy conservation law.

Applied Mechanics Reviews

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Author :
language : en
Publisher:
Release Date : 1977

Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mechanics, Applied categories.

Nonlinear Structural Mechanics

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Author : Walter Lacarbonara
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-09

Nonlinear Structural Mechanics written by Walter Lacarbonara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-09 with Science categories.

This book reviews the theoretical framework of nonlinear mechanics, covering computational methods, applications, parametric investigations of nonlinear phenomena and mechanical interpretation towards design. Builds skills via increasing levels of complexity.