On pure Willis coupling: Brillouin-zone and finite-lattice analysesa)

Area of Science:

• Physics
• Mechanical Engineering
• Materials Science

Background:

• Momentum bias in elastic media causes non-reciprocal wave propagation, known as Willis coupling.
• The role of Willis coupling as the sole mechanism and its analysis in finite structures are not well understood.

Purpose of the Study:

• To synthesize and analyze a non-reciprocal wave phenomenon driven solely by Willis coupling.
• To investigate the implications of pure Willis coupling in mechanical lattices using feedback control.

Main Methods:

• Utilized feedback control in mechanical lattices composed of masses, springs, and actuators.
• Analyzed the dynamical behavior of a unit cell from an infinite lattice chain.
• Derived analytical solutions for eigenpairs in finite lattice configurations.

Main Results:

• Successfully synthesized a non-reciprocal wave phenomenon with pure Willis coupling.
• Detailed the emergent non-reciprocal dispersion relation and quantified Brillouin-zone translation.
• Revealed the mechanism of non-reciprocity through natural frequencies and mode shapes.

Conclusions:

• Demonstrated that pure Willis coupling can induce non-reciprocity in elastic wave propagation.
• Provided a theoretical framework for understanding non-reciprocity in finite mechanical structures.
• Opened new avenues for designing advanced acoustic and mechanical metamaterials.