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Instability of Continuous Systems

Symposium Herrenalb (Germany) September 8–12, 1969

  • Conference proceedings
  • © 1971

Overview

Editors:
  1. Horst Leipholz

    1. Solid Mechanics Division, Faculty of Engineering, University of Waterloo, Waterloo, Canada

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Part of the book series: IUTAM Symposia (IUTAM)

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Table of contents (59 papers)

  1. Front Matter

    Pages I-XII
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  2. Application of Liapunov’s Direct Method to the Stability Problem of Rods Subject to Follower Forces

    • H. Leipholz
    Pages 1-10

  3. Frequency Domain Criteria for Stability of Systems Modeled by Certain Partial Differential Equations

    • J. Anton, P. Falb, M. I. Freedman
    Pages 11-14

  4. A Note on Imperfection Sensitivity of Thin Plates on a Non-linear Elastic Foundation

    • E. Reissner
    Pages 15-18

  5. A Stability Criterion for Non-linear Continua

    • P. Villaggio
    Pages 19-24

  6. L’Étude de la Stabilité Élastique et des Efforts du IIe Ordre par la Méthode des Charges Supplémentaires

    • A. Scarlat
    Pages 25-31

  7. Contributions to Hydrodynamic (In)stability by Use of the Lemma of Nagumo and Westphal

    • E. Adams
    Pages 32-40

  8. Stability Regions of Cellular Fluid Flow

    • F. H. Busse
    Pages 41-47

  9. The Stability of Gravity Waves on the Surface of a Flow with Non-uniform Velocity Distribution

    • H. G. M. Velthuizen, L. van Wijngaarden
    Pages 48-54

  10. A Non-linear Investigation of the Stability of Flow between Counter-rotating Cylinders

    • R. C. DiPrima, R. N. Grannick
    Pages 55-60

  11. On the Non-linear Stability of Plane Couette Flow

    • T. Ellingsen, B. Gjevik, E. Palm
    Pages 61-64

  12. Aeroelastic Stability of Plates and Shells: An Innocent’s Guide to the Literature

    • E. H. Dowell
    Pages 65-77

  13. Stability of Structures under Stochastic Disturbances

    • S. T. Ariaratnam
    Pages 78-84

  14. A Theory of Elastic Stability for Perfectly Elastic Materials with Couple-stresses

    • M. F. Beatty
    Pages 85-89

  15. Instability of Bars with Stress-dependent Properties

    • B. A. Boley
    Pages 90-95

  16. Trace Effects in Stability

    • H. Ziegler
    Pages 96-111

  17. A Stability Study of Continuous Systems under Parametric Excitation via Liapunov’s Direct Method

    • C. S. Hsu, T. H. Lee
    Pages 112-118

  18. Probleme nichtlinearer Operatoren bei Untersuchung der Stabilität dünner Platten und Schalen

    • R. Kodnár
    Pages 119-124

  19. Some Applications of Liapunov Functionals

    • P. C. Parks
    Pages 125-131

  20. On the Place of Energy Methods in a Global Theory of Hydrodynamic Stability

    • D. D. Joseph
    Pages 132-142
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Keywords

About this book

Until recently there was no uniform stability theory. Different approaches to stability problems had been developed in the different branches of mechanics. In the field of elasticity, it was mainly the so­ called static method and energy method which were used, while in the field of dynamics it was the kinetic method, which found its perfect expression in the theory of Liapunov. During the last few decades there has been a rapid development in the general theory of stability, stimulated, for example, by the investigations of H. ZIEGLER on elastic systems subject to non-conservative loads, and by the problems arising in aeroelasticity which are closely related to those introduced by ZIEGLER. The need was felt for kinetic methods which could also be used in investigating the stability of deformable systems. Efforts were made to adapt such methods, already known and developed in the stability theory of rigid systems, for application in the stability theory of continuous systems. During the last ten years interest was focused mainly on the application of a generalized Liapunov method to stability problems of continuous systems. All this was done in attempts to unify the various approaches to stability theory. It was with the idea of encouraging such a tendency, establishing to what extent a uniform physical and mathematical foundation already existed for stability theory in all branches of mechanics, and stimulating the further deve­ lopment of a common stability theory, that a IUTAM-Symposium was devoted to this topic.

Editors and Affiliations

  • Solid Mechanics Division, Faculty of Engineering, University of Waterloo, Waterloo, Canada

    Horst Leipholz

Bibliographic Information

  • Book Title: Instability of Continuous Systems

  • Book Subtitle: Symposium Herrenalb (Germany) September 8–12, 1969

  • Editors: Horst Leipholz

  • Series Title: IUTAM Symposia

  • DOI: https://doi.org/10.1007/978-3-642-65073-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag, Berlin/Heidelberg 1971

  • Softcover ISBN: 978-3-642-65075-8Published: 28 January 2012

  • eBook ISBN: 978-3-642-65073-4Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 422

  • Topics: Engineering, general

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