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Normal Modes and Localization in Nonlinear Systems
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Normal Modes and Localization in Nonlinear Systems - new book

ISBN: 9780792370109

ID: 978079237010

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 C/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 C/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. Books > Science and Nature List_Books, [PU: Kluwer Academic Publishers]

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Normal Modes and Localization in Nonlinear Systems - Alexander F. Vakakis
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Alexander F. Vakakis:
Normal Modes and Localization in Nonlinear Systems - new book

ISBN: 9780792370109

ID: 9780792370109

Physics; Classical Mechanics; Vibration, Dynamical Systems, Control; Ordinary Differential Equations; Partial Differential Equations beam, boundary layer, dynamical systems, dynamics, vibration Books, Springer Shop

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Normal Modes and Localization in Nonlinear Systems - Alexander F. Vakakis (Editor)
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Alexander F. Vakakis (Editor):
Normal Modes and Localization in Nonlinear Systems - hardcover

2002, ISBN: 9780792370109

ID: 585684165

Springer, 2002-01-31. 2001. Hardcover. Used:Good., Springer, 2002-01-31

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Normal Modes and Localization in Nonlinear Systems - Editor-Alexander F. Vakakis
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Editor-Alexander F. Vakakis:
Normal Modes and Localization in Nonlinear Systems - hardcover

2002, ISBN: 9780792370109

ID: 461615963

Springer, 2002-01-31. Hardcover. Good., Springer, 2002-01-31

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Normal Modes and Localization in Nonlinear Systems - Alexander F. Vakakis
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Alexander F. Vakakis:
Normal Modes and Localization in Nonlinear Systems - used book

ISBN: 9780792370109

ID: 570084015_us

Livre, [PU: Kluwer Academic Publishers]

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Details of the book
Normal Modes and Localization in Nonlinear Systems

This book contains a collection of original papers on nonlinear normal modes and localization in dynamical systems from leading experts in the field. The reader will find new analytical and computational techniques for studying normal modes and localization phenomena in nonlinear discrete and continuous oscillators. In addition, examples are provided of applications of these concepts to diverse problems of engineering and applied mathematics, such as nonlinear control of micro-gyroscopes, dynamics of floating offshore platforms, buckling of imperfect continua, order reduction of nonlinear systems, dynamics of nonlinear vibration absorbers, spatial localization and pattern formation in extended systems, singular asymptotics and nonlinear modal interactions and energy pumping in coupled oscillators.

Details of the book - Normal Modes and Localization in Nonlinear Systems


EAN (ISBN-13): 9780792370109
ISBN (ISBN-10): 0792370104
Hardcover
Paperback
Publishing year: 2002
Publisher: SPRINGER VERLAG GMBH
293 Pages
Weight: 0,785 kg
Language: eng/Englisch

Book in our database since 2009-02-03T15:16:36-05:00 (New York)
Detail page last modified on 2019-07-17T05:36:49-04:00 (New York)
ISBN/EAN: 9780792370109

ISBN - alternate spelling:
0-7923-7010-4, 978-0-7923-7010-9


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