Analysis of Nonlinear Dynamic Engineering Systems

  • W. Kleczka
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 343)


An integrated concept with numerical and symbolical parts for a detailed investigation of periodic motions of nonlinear mechanical systems described by ordinary differential equations is presented. Thereby, the local stability analysis is based upon a local approximation of the Poincaré map which has to be derived in the neighborhood of the periodic solution to be investigated. If a bifurcation takes place the system can be reduced to a critical subsystem containing all information about the local nonlinear behavior. Afterwards, the system is transformed to a nonlinear normal form which allows for a classification of the bifurcation scenario.

Beginning with the derivation of the mathematical model, the entire procedure is applied for the stability analysis of a periodically forced submerged double pendulum. Thereby, special difficulties due to the non-smooth characteristics of the damping forces have to be overcome.

The application of computer algebra software is prerequisite for the presented approach because the analytical operations and expressions become rather involved. It is of major importance that the developed computer tools are not specific to a problem.

Symbolic computation stretches the limits of analyzability far beyond a simple pen-and-paper approach. Computer power, however, is still the limiting factor because especially for high-dimensional systems computer algebra software can already operate at its limits with respect to memory requirements and computation time.

The combination of numerical and symbolical procedures is a very promising approach for a highly sophisticated analysis of nonlinear engineering problems. By means of computer-aided tools a systematic analysis of bifurcation phenomena is visible.


Periodic Solution Normal Form Hopf Bifurcation Multibody System Computer Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 1994

Authors and Affiliations

  • W. Kleczka
    • 1
  1. 1.Technical University Hamburg-HarburgHamburgGermany

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