The Method of Normal Forms. 2nd, Updated and Enlarged Edition

  • ID: 2183537
  • Book
  • 342 Pages
  • John Wiley and Sons Ltd
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In this introductory treatment the author Ali Nayfeh presents different concepts of dynamical systems theory and nonlinear dynamics. He systematically introduces models and techniques and states the relevant ranges of their validity and applicability. The text provides the reader with a clear operational framework instead of focusing on the underlying mathematical rigor. The exposition mainly features examples, which are shown through to their fianl outcome. For most of the examples, the results obtained with the method of normal forms are shown to be equivalent to to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging.

Additions to this new edition concern major topics of current interest. In particular, the author has added three new chapters dedicated to maps, bifurcations of continuous systems, and retarded systems. Especially the latter topic has gained major importance in several applications in mechanics and other areas.

From the contents:

  • SDOF Autonomous Systems
  • Systems of First–Order Equations
  • Maps
  • Bifurcations of Continuous Systems
  • Forced Oscillations of the Duffing Oscillator
  • Forced Oscillations of SDOF Systems
  • Parametrically Excited Systems
  • MDOF Systems with Quadratic Nonlinearities
  • TDOF Systems with Cubic Nonlinearities
  • Systems with Quadratic and Cubis Nonlinearities
  • Retarded Systems
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1 SDOF Autonomous Systems

2 Systems of First–Order Equations

3 Maps

4 Bifurcations of Continuous Systems

5 Forced Oscillations of the Duffing Oscillator

6 Forced Oscillations of SDOF Systems

7 Parametrically Excited Systems

8 MDOF Systems with Quadratic Nonlinearities

9 TDOF Systesm with Cubic Nonlinearities

10 Systems with Quadratic and Cubic Nonlinearities

11 Retarded Systems


Subject Index

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Ali Hasan Nayfeh received his B.S. on engineering science and his M.S. and PhD in aeronautics and astronautics from Stanford University. He established and served as Dean of the College of Engineering, Yarmouk University, Jordan from 1980–1984. He is currently University Distinguished Professor of Engineering at Virginia Polytechnic Institute and State University. He is the Editor of Wiley Series in Nonlinear Science and editor in Chief of Nonlinear Dynamics and the Journal of Vibration and Control.

Prof. Nayfeh is a fellow of the American Physical Society (APS), the American Institute of Aeronautics and Astronautics (AIAA), the American Society of Mechanical Engineers (ASME), the Society of Design and Process Science, and the American Academy of Mechanics (AAM). He holds honrary doctorates from Marine Technical University, Russia, Technical University of Munich, Germany, and Politechnika Szczecinsksa, Poland.

Prof. Nayfeh received AIAA′s Pendray Aerospace Literature Award in 1995; ASME′s J. P. Den Hartog Award in 1997; the Frank J. Maher Award for Excellence in Engineering Education in 1997; ASME′s Lyapunov Award in 2005; the Virginia Academy of Science′s Life Achievement in Science Award in 2005; the Gold Medal of Honor from the Academy of Trans–Disciplinary Learning and Advanced Studies in 2007; and the Thomas K. Caughey Dynamics Award in 2008.

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