Normal Modes And Localization In Nonlinear Systems
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Normal Modes And Localization In Nonlinear Systems
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Author : Alexander F. Vakakis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Normal Modes And Localization In Nonlinear Systems written by Alexander F. Vakakis 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 2013-06-29 with Science categories.
The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape ¢n, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape ¢n. Therefore, in the case of large-amplitude oscillations, the single-mode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1996.
Nonlinear Targeted Energy Transfer In Mechanical And Structural Systems
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Author : Alexander F. Vakakis
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-24
Nonlinear Targeted Energy Transfer In Mechanical And Structural Systems written by Alexander F. Vakakis 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 2008-12-24 with Technology & Engineering categories.
This monograph evolved over a period of nine years from a series of papers and presentations addressing the subject of passive vibration control of mechanical s- tems subjected to broadband, transient inputs. The unifying theme is Targeted - ergy Transfer – TET, which represents a new and unique approach to the passive control problem, in which a strongly nonlinear, fully passive, local attachment, the Nonlinear Energy Sink – NES, is employed to drastically alter the dynamics of the primary system to which it is attached. The intrinsic capacity of the properly - signed NES to promote rapid localization of externally applied (narrowband) - bration or (broadband) shock energy to itself, where it can be captured and dis- pated, provides a powerful strategy for vibration control and the opens the pos- bility for a wide range of applications of TET, such as, vibration and shock i- lation, passive energy harvesting, aeroelastic instability (?utter) suppression, se- mic mitigation, vortex shedding control, enhanced reliability designs (for ex- ple in power grids) and others. The monograph is intended to provide a thorough explanation of the analytical, computational and experimental methods needed to formulate and study TET in mechanical and structural systems. Several prac- cal engineering applications are examined in detail, and experimental veri?cation and validation of the theoretical predictions are provided as well. The authors also suggest a number of possible future applications where application of TET seems promising. The authors are indebted to a number of sponsoring agencies.
Modal Analysis Of Nonlinear Mechanical Systems
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Author : Gaetan Kerschen
language : en
Publisher: Springer
Release Date : 2014-10-13
Modal Analysis Of Nonlinear Mechanical Systems written by Gaetan Kerschen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-13 with Technology & Engineering categories.
The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.
Topics On The Nonlinear Dynamics And Acoustics Of Ordered Granular Media
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Author : Vakakis Alexander F
language : en
Publisher: World Scientific
Release Date : 2017-03-17
Topics On The Nonlinear Dynamics And Acoustics Of Ordered Granular Media written by Vakakis Alexander F and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-17 with Science categories.
This research monograph provides a brief overview of the authors' research in the area of ordered granular media over the last decade. The exposition covers one-dimensional homogeneous and dimer chains in great detail incorporating novel analytical tools and experimental results supporting the analytical and numerical studies. The proposed analytical tools have since been successfully implemented in studying two-dimensional dimers, granular dimers on on-site perturbations, solitary waves in Toda lattices to name a few. The second part of the monograph dwells on weakly coupled homogeneous granular chains from analytical, numerical and experimental perspective exploring the interesting phenomenon of Landau–Zener tunneling in granular media. The final part of the monograph provides a brief introduction to locally resonant acoustic metamaterials incorporating internal rotators and the resulting energy channeling mechanism in unit-cells and in one- and two-dimensional lattices. The monograph provides a comprehensive overview of the research in this interesting domain. However, this exposition is not all exhaustive with regard to equally exciting research by other researchers across the globe, but we provide an exhaustive list of references for the interested readers to further explore in this direction.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1992
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 1992 with Mechanics, Applied categories.
Iutam Symposium On Nonlinear Dynamics For Advanced Technologies And Engineering Design
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Author : Marian Wiercigroch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-11
Iutam Symposium On Nonlinear Dynamics For Advanced Technologies And Engineering Design written by Marian Wiercigroch 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 2013-01-11 with Technology & Engineering categories.
Nonlinear dynamics has been enjoying a vast development for nearly four decades resulting in a range of well established theory, with the potential to significantly enhance performance, effectiveness, reliability and safety of physical systems as well as offering novel technologies and designs. By critically appraising the state of the art, it is now time to develop design criteria and technology for new generation products/processes operating on principles of nonlinear interaction and in the nonlinear regime, leading to more effective, sensitive, accurate, and durable methods than what is currently available. This new approach is expected to radically influence the design, control and exploitation paradigms, in a magnitude of contexts. With a strong emphasis on experimentally calibrated and validated models, contributions by top-level international experts will foster future directions for the development of engineering technologies and design using robust nonlinear dynamics modelling and analysis.
Problems Of Nonlinear Mechanics And Physics Of Materials
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Author : Igor V. Andrianov
language : en
Publisher: Springer
Release Date : 2018-07-31
Problems Of Nonlinear Mechanics And Physics Of Materials written by Igor V. Andrianov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-31 with Science categories.
This book presents contributions on the current problems in a number of topical areas of nonlinear dynamics and physics, written by experts from Russia, Ukraine, Israel, Germany, Poland, Italy, the Netherlands, the USA, and France. The book is dedicated to Professor Leonid I. Manevitch, an outstanding scholar in the fields of Mechanics of Solids, Nonlinear Dynamics, and Polymer Physics, on the occasion of his 80th birthday.
Modal Analysis Topics Volume 3
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Author : Tom Proulx
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-18
Modal Analysis Topics Volume 3 written by Tom Proulx 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 2011-03-18 with Technology & Engineering categories.
Modal Analysis Topics Volume 3. Proceedings of the 29th IMAC, A Conference and Exposition on Structural Dynamics, 2011, the third volume of six from the Conference, brings together over 30 contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics.
Topics In Nonlinear Dynamics Volume 1
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Author : Gaetan Kerschen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-24
Topics In Nonlinear Dynamics Volume 1 written by Gaetan Kerschen 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 2013-05-24 with Technology & Engineering categories.
Topics in Nonlinear Dynamics, Volume 1: Proceedings of the 31st IMAC, A Conference and Exposition on Structural Dynamics, 2013, the first volume of seven from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Nonlinear Oscillations Nonlinearities ... In Practice Nonlinear System Identification: Methods Nonlinear System Identification: Friction & Contact Nonlinear Modal Analysis Nonlinear Modeling & Simulation Nonlinear Vibration Absorbers Constructive Utilization of Nonlinearity
Dynamics Of Very High Dimensional Systems
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Author : Earl H Dowell
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-08-22
Dynamics Of Very High Dimensional Systems written by Earl H Dowell and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-22 with Technology & Engineering categories.
Many books on dynamics start with a discussion of systems with one or two degrees of freedom and then turn to the generalization to the case of many degrees of freedom. For linear systems, the concept of eigenfunctions provides a compact and elegant method for decomposing the dynamics of a high dimensional system into a series of independent single-degree-of-freedom dynamical systems. Yet, when the system has a very high dimension, the determination of the eigenfunctions may be a distinct challenge, and when the dynamical system is nonconservative and/or nonlinear, the whole notion of uncoupled eigenmodes requires nontrivial extensions of classical methods. These issues constitute the subject of this book.