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Modulation instability in nonlinear flexible mechanical metamaterials
A Demiquel1, V Achilleos1, G Theocharis1
1Laboratoire d'Acoustique de l'Université du Mans (LAUM), UMR 6613, Institut d'Acoustique - Graduate School (IA-GS), CNRS, Le Mans Université, France.
Physical Review. E
|June 17, 2023
Summary
This study investigates modulation instabilities (MI) in flexible mechanical metamaterials (flexMMs). We mapped MI occurrence and highlighted the crucial role of rotation-displacement coupling in flexMMs for wave stability.
Area of Science:
- Nonlinear mechanics
- Mechanical metamaterials
- Wave propagation
Background:
- Flexible mechanical metamaterials (flexMMs) exhibit complex behaviors under dynamic loading.
- Understanding wave propagation and stability in discrete metamaterial chains is crucial for designing advanced materials.
Purpose of the Study:
- To investigate modulation instabilities (MI) in a one-dimensional flexMM chain.
- To derive an effective nonlinear Schrödinger equation for rotational waves.
- To establish a parameter map for MI occurrence.
Main Methods:
- Lumped element approach to model flexMMs.
- Multiple-scales method for deriving the effective nonlinear equation.
- Numerical simulations of the discrete nonlinear problem.
Main Results:
- Derived an effective nonlinear Schrödinger equation for rotational waves in flexMMs.
- Established a map correlating MI occurrence with metamaterial parameters and wave numbers.
- Identified the significant role of rotation-displacement coupling in MI manifestation.
Conclusions:
- The study provides a theoretical framework and numerical validation for MI in flexMMs.
- Results offer design guidelines for nonlinear metamaterials, enabling control over wave stability or instability.
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