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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.