Nonlinear Stability and Bifurcation Theory: An Introduction for Engineers and Applied Scientists - Softcover

Troger, Hans; Steindl, Alois

Softcover

ISBN 10: 3211822925 ISBN 13: 9783211822920

Publisher: Springer, 1991

Synopsis

Every student in engineering or in other fields of the applied sciences who has passed through his curriculum knows that the treatment of nonlin­ ear problems has been either avoided completely or is confined to special courses where a great number of different ad-hoc methods are presented. The wide-spread believe that no straightforward solution procedures for nonlinear problems are available prevails even today in engineering cir­ cles. Though in some courses it is indicated that in principle nonlinear problems are solveable by numerical methods the treatment of nonlinear problems, more or less, is considered to be an art or an intellectual game. A good example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. At the beginning of the seventies, start­ ing with the work of V.1. Arnold, R. Thom and many others, new ideas which, however, have their origin in the work of H. Poincare and A. A. Andronov, in the treatment of nonlinear problems appeared. These ideas gave birth to the term Bifurcation Theory. Bifurcation theory allows to solve a great class of nonlinear problems under variation of parameters in a straightforward manner.

About this title

Synopsis

This study aims to make progress in the field of stability theory available to scientists and engineers. A treatment of the different types of loss of stability of equilibrium positions of static and dynamic systems and of periodic solutions of dynamic systems is given by means of the methods of bifurcation and singuality theory. The reader needs only a background in mathematics. Among others, concepts such as centre manifold theory, the method of Ljapunov-Schmidt, normal form theory, unfolding theory, bifurcation diagrams, classifications and bifurcations in symmetric systems are discussed, as far as they are relevant in applications. Most important for the whole representation is a set of examples taken from mechanics and engineering showing the usefulness of the above mentioned concepts. These examples include buckling problems of rods, plates and shells, the loss of stability of the motion of road and rail vehicles, of a simple robot, and of fluid conveying elastic tubes. With these examples, questions like symmetry breaking, pattern formation, imperfection sensitivity, transition to chaos and correct modelling of systems are explored.

Finally, a number of selected FORTRAN-routines should encourage readers to apply these theories to their own individual problems.

Edition details

• Publisher: Springer
• Publication date: 1991
• ISBN 10: 3211822925
• ISBN 13: 9783211822920
• Binding: Paperback
• Language: English
• Number of pages: 418