Instability of Continuous Systems

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.

Application of Liapunov’s direct method to the stability problem of rods subject to follower forces.- Frequency domain criteria for stability of systems modeled by certain partial differential equations.- A note on imperfection sensitivity of thin plates on a nonlinear elastic foundation.- A stability criterion for non-linear continua.- L’étude de la stabilité élastique et des efforts du IIe ordre par la méthode des charges supplémentaires.- Contributions to hydrodynamic (in)stability by use of the lemma of Nagumo and Westphal.- Stability regions of cellular fluid flow.- The stability of gravity waves on the surface of a flow with non-uniform velocity distribution.- A non-linear investigation of the stability of flow between counter-rotating cylinders.- On the non-linear stability of plane Couette flow.- Aeroelastic stability of plates and shells: an innocent’s guide to the literature.- Stability of structures under stochastic disturbances.- A theory of elastic stability for perfectly elastic materials with couple-stresses.- Instability of bars with stress-dependent properties.- Trace effects in stability.- A stability study of continuous systems under parametric excitation via Liapunov’s direct method.- Probleme nichtlinearer Operatoren bei Untersuchung der Stabilität dünner Platten und Schalen.- Some applications of Liapunov functional.- On the place of energy methods in a global theory of hydrodynamic stability.- Interfacial instability between fluids and granular beds.- Unstable flows in two dimensions: comparison of laboratory experiments with numerical simulation.- On the effect of sidewalls in cellular convection.- The stability of cellular branching solutions of the Navier-Stokes equations.- On equilibrium states and periodic vibrations of thin nonlinear elastic systems.- On buckling and instability of plastic structural models.- A contribution to a linearized engineering shell theory.- Stability of the Cosserat surface.- On the stability of periodic solutions in fluid mechanics.- On general theorems for stability.- An invariance principle for dynamical systems on Banach space: application to the general problem of thermoelastic stability.- On the possibility of subcritical instabilities.- Feedback stabilization of distributive systems with applications to plasma stabilization.- Determinism and uncertainty in stability.- Hölder stability and logarithmic convexity.- Thermoelastic stability of a finitely deformed solid under nonconservative loads.- Examples on the stabilizing and destabilizing effects.- Stability conditions of rigid-plastic solids with extension to visco-plasticity.- On the dynamical stability of fluid phases.- Review of the finite bandwidth concept.- A class of unsteady nonlinear waves in parallel flows.- Optimal structural design in non-conservative problems of elastic stability.- Zur Stabilität des schwingenden Tragflügels im Unterschallbereich.- Finite amplitude response of circular plates subject to dynamic loading.- Equilibrium and stability of elastic-plastic bodies.- Instability under cycles of plastic deformation.- Coupled modes of buckling in some continuous systems.- Perturbation patterns in nonlinear branching theory.- Non-conservative effects produced by thrust of jet engine.- Stability of viscoelastic systems subjected to nonconservative forces.- The instability of pipe Poiseuille flow with respect to finite amplitude disturbances.- The structure of the damping disturbances in the stability of unbounded laminar flows.- Linear dynamical systems in Hilbert space.- On the stability of constant profile waves.- A theory of elasto-plastic buckling of structures.- Buckling and postbuckling behavior of initially imperfect orthotropic cylindrical shells under axial compression and internal pressure.- Instabilität der Ruhelage für ein System mit zwei Freiheitsgraden.- Substantiation of the theory of stability of cylindrical shells on the basis of the Gauss principle.- On structural instability due to strainsoftening.- Asymptotic stability of travelling waves.