Equilibrium and stability of coupled nonlinear energy-storing components

Area of Science:

• Multidisciplinary research spanning physics, engineering, and materials science.
• Focus on nonlinear dynamics, complex systems, and physical intelligence.

Background:

• Coupled nonlinear systems exhibit complex behaviors like multistability and memory, crucial for physical intelligence.
• Predicting equilibrium states and stability in these systems is challenging due to complex energy landscapes and multiple equilibria.

Purpose of the Study:

• To introduce a general static framework for visualizing and analyzing equilibrium states in coupled nonlinear systems.
• To enable systematic exploration of equilibrium landscapes and improve the design of systems with emergent functional behavior.

Main Methods:

• Developed a parametric space where element-level equilibria form a one-dimensional manifold representing system-level equilibria.
• Combined parametric space formulation with continuation strategy and local stability assessment.
• Traced both stable and unstable equilibria, including isolated states inaccessible by standard methods.

Main Results:

• The proposed framework allows unambiguous visualization of system equilibria, overcoming limitations of conventional displacement maps.
• Experimental validation in mechanical systems (nonlinear springs, inflatable structures) showed quantitative agreement between predictions and measurements.
• Successfully traced stable, unstable, and isolated equilibria.

Conclusions:

• The unifying static framework provides a powerful tool for analyzing and designing complex nonlinear coupled systems.
• Enables systematic exploration of equilibrium landscapes, advancing the field of physical intelligence and structural design.