Normal Modes and Localization in Nonlinear Systems

Editors: Vakakis, Alexander F. (Ed.)

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About this book

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.

Table of contents (15 chapters)

Table of contents (15 chapters)
  • Invariant Manifolds, Nonclassical Normal Modes, and Proper Orthogonal Modes in the Dynamics of the Flexible Spherical Pendulum

    Georgiou, Ioannis T. (et al.)

    Pages 3-31

  • Normal Vibrations in Near-Conservative Self-Excited and Viscoelastic Nonlinear Systems

    Mikhlin, Yu. V. (et al.)

    Pages 33-48

  • Nonlinear Normal Modes in a System with Nonholonomic Constraints

    Rand, R. H. (et al.)

    Pages 49-64

  • Nonlinear Normal Modes of a Parametrically Excited Cantilever Beam

    Yabuno, Hiroshi (et al.)

    Pages 65-77

  • Normal Modes and Boundary Layers for a Slender Tensioned Beam on a Nonlinear Foundation

    Pellicano, F. (et al.)

    Pages 79-93

Buy this book

eBook 118,99 €
price for China (P.R.) (gross)
  • ISBN 978-94-017-2452-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 139,99 €
price for China (P.R.) (gross)
  • ISBN 978-0-7923-7010-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover 139,99 €
price for China (P.R.) (gross)
  • ISBN 978-90-481-5715-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Normal Modes and Localization in Nonlinear Systems
Editors
  • Alexander F. Vakakis
Copyright
2001
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-2452-4
DOI
10.1007/978-94-017-2452-4
Hardcover ISBN
978-0-7923-7010-9
Softcover ISBN
978-90-481-5715-0
Edition Number
1
Number of Pages
VI, 294
Additional Information
Reprinted from NONLINEAR DYNAMICS, 25:1-3
Topics