On the experimental identification of unstable static equilibria

Area of Science:

• Solid Mechanics
• Nonlinear Dynamics
• Continuum Mechanics

Background:

• Elastic continua can possess multiple equilibrium configurations, including stable and unstable states.
• Axially loaded beams beyond their critical load exhibit buckled stable states separated by unstable equilibria.
• Lateral loading or dynamic impacts can induce snap-through behavior between these configurations.

Purpose of the Study:

• To demonstrate how transient dynamics reveal the presence of unstable equilibrium configurations in elastic systems.
• To analyze the behavior of trajectories near unstable equilibria under dynamic loading.
• To provide a method for identifying unstable states in higher-order or continuous systems.

Main Methods:

• Investigating the response of an axially and laterally loaded beam (shallow arch) to dynamic impacts.
• Simulating transient trajectories initiated by perturbations of varying strength and location.
• Analyzing the phase space exploration and energy behavior of these trajectories.

Main Results:

• Transient trajectories exhibit characteristic slowdowns when approaching unstable equilibrium configurations.
• The presence of unstable equilibria influences the exploration of the system's phase space.
• This phenomenon is observable even in complex, continuous systems and noisy experimental settings.

Conclusions:

• Transient dynamics provide a viable method for identifying unstable equilibrium configurations in elastic continua.
• Understanding these dynamics is crucial for predicting system behavior under impact loading.
• The findings offer insights into the dynamics of systems with potential energy barriers.