Normal Modes and Localization in Nonlinear Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Normal Modes and Localization in Nonlinear Systems write by Alexander F. Vakakis. This book was released on 2013-06-29. Normal Modes and Localization in Nonlinear Systems available in PDF, EPUB and Kindle. 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
Normal Modes and Localization in a Class of Nonlinear Continuous Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Normal Modes and Localization in a Class of Nonlinear Continuous Systems write by Melvin Eugene King. This book was released on 1993. Normal Modes and Localization in a Class of Nonlinear Continuous Systems available in PDF, EPUB and Kindle.
Analytical Amd Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization
Analytical Amd Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytical Amd Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization write by Melvin Eugene King. This book was released on 1995. Analytical Amd Experimental Aspects of Nonlinear Normal Modes and Nonlinear Mode Localization available in PDF, EPUB and Kindle. 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
Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems write by Alexander F. Vakakis. This book was released on 2008-12-24. Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems available in PDF, EPUB and Kindle. 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
Modal Analysis of Nonlinear Mechanical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modal Analysis of Nonlinear Mechanical Systems write by Gaetan Kerschen. This book was released on 2014-10-13. Modal Analysis of Nonlinear Mechanical Systems available in PDF, EPUB and Kindle. 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.
