Explanation to the Lecture Theory of Kinetic Stability for Structures

Content:
Definition of stability by Lyapunov
• Demonstrative definition of stability
• Lyapunov’s definition of stability
• Asymptotic stability

First Method
• Imperfection and disturbed bifurcation
• Method of small vibrations
• Imperfection sensitivity of symmetric, non-symmetric and oblique bifurcation
• Stability degree and practical instability
• Unilateral constraints
• Alternating constraints
• Direction dependent force laws
• Bifurcation from the non-trivial state
• Interaction

Second method
• Energy integral
• Principle of minimum of potential energy
• Inner and outer potential (examples)
• Analogy to the motion of a sphere
• Zero natural values
• Non-linear constraints
• Sensitivity of equilibrium states
• Local and global instability
• Transition from stress problems to stability problems

Plastic buckling
• Discussion in phase space