Non-Newtonian Topological Mechanical Metamaterials Using Feedback Control.

Area of Science:

• * Mechanical metamaterials
• * Topological physics
• * Control theory

Background:

• * Traditional mechanical systems adhere to Newtonian dynamics.
• * Topological phases, like those in the quantum Haldane model, exhibit unique properties such as chiral edge modes.
• * Implementing nonreciprocal couplings, essential for some topological phases, challenges classical mechanics due to Newton's third law.

Purpose of the Study:

• * To introduce a method for designing topological mechanical metamaterials unbound by Newtonian constraints.
• * To demonstrate the realization of topological phases, specifically a modified Haldane model, in mechanical systems.
• * To showcase the flexibility of the proposed platform for realizing diverse lattice parameters.

Main Methods:

• * Employing active feedback forces on unit cells within a mechanical lattice.
• * Utilizing autonomous controllers for real-time local response generation.
• * Implementing closed-loop control to overcome limitations of Newton's third law.

Main Results:

• * Achieved a topological phase with chiral edge modes in an analogous mechanical system.
• * Realized a modified Haldane model in a mechanical metamaterial with specific complex-valued couplings.
• * Demonstrated that edge modes propagate unidirectionally, balanced by counterpropagating bulk modes.

Conclusions:

• * The proposed method offers a general and flexible platform for designing advanced mechanical metamaterials.
• * This approach allows for the realization of complex lattice parameters, including nonlocal, nonlinear, time-dependent, and non-Hermitian dynamics.
• * Opens new avenues for exploring topological phenomena in classical mechanical systems.