Normal Modes And Localization In Nonlinear Systems

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Normal Modes and Localization in Nonlinear Systems

Author : Alexander F. Vakakis
Publisher : Springer Science & Business Media
ISBN 13 : 9401724520
Total Pages : 290 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Normal Modes and Localization in Nonlinear Systems by : Alexander F. Vakakis

Download or read book Normal Modes and Localization in Nonlinear Systems written by Alexander F. Vakakis and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 a Class of Nonlinear Continuous Systems

Author : Melvin Eugene King
Publisher :
ISBN 13 :
Total Pages : 106 pages
Book Rating : 4.:/5 (293 download)

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Book Synopsis Normal Modes and Localization in a Class of Nonlinear Continuous Systems by : Melvin Eugene King

Download or read book Normal Modes and Localization in a Class of Nonlinear Continuous Systems written by Melvin Eugene King and published by . This book was released on 1993 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytical Amd Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization

Author : Melvin Eugene King
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (774 download)

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Book Synopsis Analytical Amd Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization by : Melvin Eugene King

Download or read book Analytical Amd Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization written by Melvin Eugene King and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, several aspects of nonlinear normal modes (NNMs) and free and forced nonlinear mode localization are investigated. In the first phase of the work, new asymptotic methodologies based on the concept of NNM are developed in order to compute synchronous responses for two classes of conservative nonlinear systems; namely (i) periodic systems composed of repeated sub-structural elements and (ii) systems possessing internal resonances. For coupled repetitive systems, NNMs are shown to provide an excellent framework by which to study the nonlinear mode localization phenomenon, wherein vibrational energy is spatially confined to a limited number of sub-structures, and criteria are established in order to detect these localized normal modes. Internal resonances have provided somewhat of an obstacle in existing NNM methodologies, thus modifications of the energy-based NNM methodology are also developed in order to appropriately account for resonant interactions. Several applications of these methodologies are considered. The second phase of this thesis is concerned with analytical and experimental studies of localization in cyclic and non-cyclic periodic systems. Examples of such systems encountered in engineering practice include bladed disk assemblies, large space structures composed of repeated bays and periodically stiffened plates and shells such as those found in airplane fuselages. Extensive work in the literature has focused on localization in linear systems, from which two necessary ingredients for the existence of localized modes have been identified: weak sub-structure coupling and weak structural mistunings. In the present work, free and forced mode localization are investigated in periodic systems whose sub-structures are weakly nonlinear. In contrast to linear theory, nonlinear mode localization is shown to exist in the absence of any structural mistunings (i.e. in perfectly periodic systems). In an effort to verify some of the analytical localization results, an experimental investigation of steady-state localization in a flexible system with active stiffness nonlinearities is performed. It is hoped that this work provides a first step toward the development of new approaches to passive and/or active vibration and shock isolation designs based on the concepts of NNMs and nonlinear mode localization.

Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems

Author : Alexander F. Vakakis
Publisher : Springer Science & Business Media
ISBN 13 : 1402091303
Total Pages : 1030 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems by : Alexander F. Vakakis

Download or read book Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems written by Alexander F. Vakakis and published by Springer Science & Business Media. This book was released on 2008-12-24 with total page 1030 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Gaetan Kerschen
Publisher : Springer
ISBN 13 : 3709117917
Total Pages : 346 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Modal Analysis of Nonlinear Mechanical Systems by : Gaetan Kerschen

Download or read book Modal Analysis of Nonlinear Mechanical Systems written by Gaetan Kerschen and published by Springer. This book was released on 2014-10-13 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analytical and Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization

Author : Melvin Eugene King
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.:/5 (357 download)

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Book Synopsis Analytical and Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization by : Melvin Eugene King

Download or read book Analytical and Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization written by Melvin Eugene King and published by . This book was released on 1995 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topics On The Nonlinear Dynamics And Acoustics Of Ordered Granular Media

Author : Yuli Starosvetsky
Publisher : World Scientific
ISBN 13 : 981322195X
Total Pages : 640 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Topics On The Nonlinear Dynamics And Acoustics Of Ordered Granular Media by : Yuli Starosvetsky

Download or read book Topics On The Nonlinear Dynamics And Acoustics Of Ordered Granular Media written by Yuli Starosvetsky and published by World Scientific. This book was released on 2017-03-17 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author :
Publisher :
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.3/5 (243 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1992 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design

Author : Marian Wiercigroch
Publisher : Springer Science & Business Media
ISBN 13 : 9400757425
Total Pages : 442 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design by : Marian Wiercigroch

Download or read book IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design written by Marian Wiercigroch and published by Springer Science & Business Media. This book was released on 2013-01-11 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Igor V. Andrianov
Publisher : Springer
ISBN 13 : 3319922343
Total Pages : 530 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Problems of Nonlinear Mechanics and Physics of Materials by : Igor V. Andrianov

Download or read book Problems of Nonlinear Mechanics and Physics of Materials written by Igor V. Andrianov and published by Springer. This book was released on 2018-07-31 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Nonlinear Dynamics

Author : José Roberto Castilho Piqueira
Publisher : Springer Nature
ISBN 13 : 3031451015
Total Pages : 352 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Lectures on Nonlinear Dynamics by : José Roberto Castilho Piqueira

Download or read book Lectures on Nonlinear Dynamics written by José Roberto Castilho Piqueira and published by Springer Nature. This book was released on 2024-01-03 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, nonlinear modal analysis and model reduction, synchronization, and strongly nonlinear dynamics. Interwoven seamlessly, these groups cover a wide range of topics, from fundamental concepts to practical applications, catering to both introductory and advanced readers. The first group, consisting of chapters 1 and 2, serves as an introduction to the theory of parametric resonance and the dynamics of parametrically excited slender structures. Chapters 3, 4, and 5 form the second group, offering insights into normal forms, nonlinear normal modes, and nonlinear system identification. Chapters 6 and 7 delve into asynchronous modes of structural vibration and master-slave topologies for time signal distribution within synchronous systems, respectively, representing the third group. Finally, the last four chapters tackle the fourth group, exploring nonlinear dynamics of variable mass oscillators, advanced analytical methods for strong nonlinear vibration problems, chaos theory, and dynamic integrity from the perspectives of safety and design. This book harmoniously combines theoretical depth and practical relevance to provide a comprehensive understanding of nonlinear dynamics.

Modal Analysis Topics, Volume 3

Author : Tom Proulx
Publisher : Springer Science & Business Media
ISBN 13 : 1441992995
Total Pages : 568 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Modal Analysis Topics, Volume 3 by : Tom Proulx

Download or read book Modal Analysis Topics, Volume 3 written by Tom Proulx and published by Springer Science & Business Media. This book was released on 2011-03-18 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Wave Motion, Intelligent Structures And Nonlinear Mechanics

Author : Ardeshir Guran
Publisher : World Scientific
ISBN 13 : 981450100X
Total Pages : 325 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Wave Motion, Intelligent Structures And Nonlinear Mechanics by : Ardeshir Guran

Download or read book Wave Motion, Intelligent Structures And Nonlinear Mechanics written by Ardeshir Guran and published by World Scientific. This book was released on 1995-06-09 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : David Wagg
Publisher : Springer
ISBN 13 : 3319106449
Total Pages : 461 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Nonlinear Vibration with Control by : David Wagg

Download or read book Nonlinear Vibration with Control written by David Wagg and published by Springer. This book was released on 2014-11-03 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

Author : Leonid I. Manevitch
Publisher : Springer
ISBN 13 : 9811046662
Total Pages : 448 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures by : Leonid I. Manevitch

Download or read book Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures written by Leonid I. Manevitch and published by Springer. This book was released on 2017-07-25 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Dynamics

Author : Ardshir Guran
Publisher : World Scientific
ISBN 13 : 9789810229825
Total Pages : 254 pages
Book Rating : 4.2/5 (298 download)

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Book Synopsis Nonlinear Dynamics by : Ardshir Guran

Download or read book Nonlinear Dynamics written by Ardshir Guran and published by World Scientific. This book was released on 1997 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers on the subject of nonlinear dynamics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this fast-growing field. The topics covered include chaos, tools to analyze motions, fractal boundaries, dynamics of the Fitzhugh-Nagumo equation, structural control, separation of contaminations from signal of interest, parametric excitation, stochastic bifurcation, mode localization in repetitive structures, Toda lattice, transition from soliton to chaotic motion, nonlinear normal modes, noise perturbations of nonlinear dynamical systems, and phase locking of coupled limit cycle oscillators. Mathematical methods include Lie transforms, Monte Carlo simulations, stochastic calculus, perturbation methods and proper orthogonal decomposition. Applications include gyrodynamics, tether connected satellites, shell buckling, nonlinear circuits, volume oscillations of a large lake, systems with stick-slip friction, imperfect or disordered structures, overturning of rigid blocks, central pattern generators, flow induced oscillations, shape control and vibration suppression of elastic structures.All of these diverse contributions have a common thread: the world of nonlinear behavior. Although linear dynamics is an invaluable tool, there are many problems where nonlinear effects are essential. Some examples include bifurcation of solutions, stability of motion, the effects of large displacements, and subharmonic resonance. This book shows how nonlinear dynamics is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.

Normal Modes in Nonlinear Nonsymmetrical Systems with Two Degrees of Freedom, and Applications to Air Springs

Author : Mahmoud Abd-Elfattah Moustafa
Publisher :
ISBN 13 :
Total Pages : 250 pages
Book Rating : 4.:/5 (185 download)

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Book Synopsis Normal Modes in Nonlinear Nonsymmetrical Systems with Two Degrees of Freedom, and Applications to Air Springs by : Mahmoud Abd-Elfattah Moustafa

Download or read book Normal Modes in Nonlinear Nonsymmetrical Systems with Two Degrees of Freedom, and Applications to Air Springs written by Mahmoud Abd-Elfattah Moustafa and published by . This book was released on 1965 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear vibrations of systems having two degrees of freedom has met considerable attention during the past few years. Nonlinear symmetrical systems have received most of it. Normal mode motion of a system is defined as a periodic motion such that the masses of the system assume repeated displacements after some interval of time, called the period of oscillation. In this kind of motion there is a definite relation between the displacements of the masses which is called the modal relation. The modal line is defined as the locus of all points, in the plane representing the displacements, which set the system in normal mode motion when started from rest. This line passes through the origin of the plane. Systems vibrating in normal modes have also what is called the orthogonality property. That is, the modal relation curves intersect the total energy line orthogonally. There exists a type of normal mode which has a straight modal relation. The linear systems belong to it. In this type of mode the orthogonality property is used to determine the modal relations and this in turn enables the equations of motion to be decoupled to form two separate systems, each with a single degree of freedom. This of course simplifies analysis of the system. Generally speaking the modal relations are not straight and they could be determined easily by numerical means. For this purpose an algorithm for determining the normal mode motions was developed. The application of the orthogonality property is also useful when applied to small displacements. One striking phenomenon have more normal modes than The existence of this excess of of nonlinear systems is that they may the number of degrees of freedom. modes can be easily detected by using the orthogonality property. The stability of systems oscillating in normal modes could be studied by using Liapounovrs theorem of stability. The total energy equation of a dynamical system is a Liapounov function. The idea of the modal phase plane, which is a plot of the total energy line and the modal line, is introduced. This helps in deducing the stability of normal modes. The concepts of singularities in this plane are defined. The mathematical procedure for determining the normal modes was applied to an air spring system with two degrees of freedom. An experimental apparatus was constructed to compare the theoretical and the experimental results. This comparison showed fair agreement. The forced motion of the air spring system was studied experimentally. Over some range of the exciting frequency two resonances appeared. Each one corresponds to one normal mode. The results showed that the system eventually oscillates essentially in normal modes when the exciting frequency is equal to a natural frequency of the system.