Nonreciprocal wave phenomena in spring-mass chains with effective stiffness modulation induced by geometric...

Area of Science:

• Acoustics
• Nonlinear Dynamics
• Metamaterials

Background:

• Acoustic nonreciprocity enables effects like immunity from backscattering and unidirectional band gaps.
• Spatiotemporal modulation of material properties is a key method to break acoustic reciprocity.
• Nonlinear deformations can modulate effective material properties for wave propagation.

Purpose of the Study:

• To present a model for acoustic nonreciprocity using a nonlinear deformation.
• To investigate the propagation of small-amplitude waves in a modulated medium.
• To explore the design of direction-dependent acoustic devices.

Main Methods:

• Modeling a discrete spring-mass chain with large, slow nonlinear deformation.
• Applying multiple-scale perturbation analysis to derive effective wave equations.
• Conducting direct numerical simulations to validate the model.

Main Results:

• Small-amplitude waves in the modulated medium are described by a linear monatomic chain with space- and time-dependent stiffness.
• The modulation depth is tunable via geometric and stiffness parameters of the unit cell.
• Numerical simulations confirm the accuracy of the small-on-large approximation.

Conclusions:

• Acoustic nonreciprocity can be achieved through slow nonlinear deformations in discrete systems.
• The developed model accurately describes wave propagation in such modulated media.
• This work provides a foundation for designing novel acoustic devices with directional control.