Modelling of Mechanical Systems: Discrete Systems


  • Francois Axisa, Professor of Mechanical Engineering at ENSTA, France

This first volume is concerned with discrete systems – the study of which constitutes the cornerstone of all mechanical systems, linear or non-linear. It covers the formulation of equations of motion and the systematic study of free and forced vibrations. The book goes into detail about subjects such as generalized coordinates and kinematical conditions; Hamilton’s principle and Lagrange equations; linear algebra in N-dimensional linear spaces and the orthogonal basis of natural modes of vibration of conservative systems. Also included are the Laplace transform and forced responses of linear dynamical systems, the Fourier transform and spectral analysis of excitation and response deterministic signals.Forthcoming volumes in this series:Vol II: Structural Elements; to be published in June 2005Vol III: Fluid-structure Interactions; to be published in August 2006Vol IV: Flow-induced Vibrations; to be published in August 2007
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Mechanical engineers and designers, and specialists in damage mechanics, fluid-structure interaction, vibration effects and applied mechanics


Book information

  • Published: November 2003
  • ISBN: 978-1-903996-51-5


‘For this is not just a translation; much has been added, refined and polished, to make this book an excellent addition to anyone’s bookshelf, whose interests lie in Dynamics, Vibrations, or Fluid Structure Interactions.’ Michael Païdoussis, Emeritus Professor in the Department of Mechanical Engineering, McGill University, Canada, in the Journal of Fluids and Structures, 2004

Table of Contents

Chapter 1. Mechanical systems and equilibrium of forcesChapter 2. Principle of virtual work and Lagrange’s equationsChapter 3. Hamilton’s Principle and Lagrange’s equations of unconstrained systemsChapter 4. Constrained systems and Lagrange’s undetermined multipliersChapter 5. Autonomous oscillatorsChapter 6. Multi-degree-of-freedom systems: natural modes of vibrationChapter 7. Forced vibration: response to transient excitationsChapter 8. Spectral analysis of deterministic time signalsChapter 9. Spectral analysis of forced vibrations