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: John Wiley & Sons
Release Date : 2008-07-11
Normal Modes And Localization In Nonlinear Systems written by Alexander F. Vakakis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-11 with Science categories.
This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.
Normal Modes And Localization In Nonlinear Systems
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Author : Alexander F. Vakakis
language : en
Publisher: Springer
Release Date : 2013-01-11
Normal Modes And Localization In Nonlinear Systems written by Alexander F. Vakakis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 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.
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.
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
Nonlinear Dynamics Volume 1
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Author : Gaëtan Kerschen
language : en
Publisher: Springer
Release Date : 2015-08-14
Nonlinear Dynamics Volume 1 written by Gaëtan Kerschen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-14 with Technology & Engineering categories.
Nonlinear Dynamics, Volume 1. Proceedings of the 33rd IMAC, A Conference and Exposition on Balancing Simulation and Testing, 2015, the first volume of ten 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 Nonlinear Simulation Using Harmonic Balance Nonlinear Modal Analysis Nonlinear System Identification Nonlinear Modeling & Simulation Nonlinearity in Practice Nonlinear Systems Round Robin on Nonlinear System Identification.
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.
Wave Motion Intelligent Structures And Nonlinear Mechanics
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Author : Ardeshir Guran
language : en
Publisher: World Scientific
Release Date : 1995-06-09
Wave Motion Intelligent Structures And Nonlinear Mechanics written by Ardeshir Guran and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-06-09 with Technology & Engineering categories.
This book is a collection of papers on the subject of applied system dynamics and control written by experts in this field. It offers the reader a sampling of exciting research areas in three fast-growing branches: (i) Wave Motion (ii) Intelligent Structures (iii) Nonlinear Mechanics. The topics covered include flow instability, nonlinear mode localization autoparametric systems with pendula, and geometric stiffening in multibody dynamics. Mathematical methods include perturbation methods, modern control theory, nonlinear neural nets, and resonance scattering theory of Überall-Ripoche-Maze. Applications include sound-induced structural vibrations, fiber acoustic waveguides, vibration suppression of structures, linear control of gyroscopic systems, and nonlinear control of distributed systems.This book shows how applied system dynamics and control is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.
Nonlinear Vibration With Control
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Author : David Wagg
language : en
Publisher: Springer
Release Date : 2014-11-03
Nonlinear Vibration With Control written by David Wagg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-03 with Technology & Engineering categories.
This book provides a comprehensive discussion of nonlinear multi-modal structural vibration problems, and shows how vibration suppression can be applied to such systems by considering a sample set of relevant control techniques. It covers the basic principles of nonlinear vibrations that occur in flexible and/or adaptive structures, with an emphasis on engineering analysis and relevant control techniques. Understanding nonlinear vibrations is becoming increasingly important in a range of engineering applications, particularly in the design of flexible structures such as aircraft, satellites, bridges, and sports stadia. There is an increasing trend towards lighter structures, with increased slenderness, often made of new composite materials and requiring some form of deployment and/or active vibration control. There are also applications in the areas of robotics, mechatronics, micro electrical mechanical systems, non-destructive testing and related disciplines such as structural health monitoring. Two broader themes cut across these application areas: (i) vibration suppression – or active damping – and, (ii) adaptive structures and machines. In this expanded 2nd edition, revisions include: An additional section on passive vibration control, including nonlinear vibration mounts. A more in-depth description of semi-active control, including switching and continuous schemes for dampers and other semi-active systems. A complet e reworking of normal form analysis, which now includes new material on internal resonance, bifurcation of backbone curves and stability analysis of forced responses. Further analysis of the nonlinear dynamics of cables including internal resonance leading to whirling. Additional material on the vibration of systems with impact friction. The book is accessible to practitioners in the areas of application, as well as students and researchers working on related topics. In particular, the aim is to introduce the key concepts of nonlinear vibration to readers who have an understanding of linear vibration and/or linear control, but no specialist knowledge in nonlinear dynamics or nonlinear control.
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.