When designing structures and mechanical systems, it is imperative to control the risks of instability arising from many phenomena. Mention may in particular be made of the various couplings of a non-conservative nature related to the existence of friction or of contact between a moving elastic structure and a fluid or a solid. Moreover, the phenomena of buckling and blistering are increasingly dimensioning given the lightening of the structures associated with the use of new materials. In the fields of transport, civil engineering and energy, we can cite: brake noise, resistance to crashes, instabilities of rotating machines, risk of building collapse, stability of drilling systems.
I. Introduction and illustration from industries II. Buckling of elastic structures III. Non-conservative elastic structures IV. Stability of mechanical systems and vibration V. Practical methodology in engineering and research units. VI. Applications to mechanical systems with friction and structures coupled with flow