Wave propagation in multistable magneto-elastic lattices

Significance statement

Nonlinearities from magnetic interactions have not yet been used to produce engineered topology changing structures with adaptable wave propagation properties. Therefore, this paper presents how the multistability of magneto-elastic interactions can be exploited in for changing the in-plane wave propagation properties of periodic structures. We expect that it will have applications in novel control of wave energy for uses including energy dissipation, impact protection, and energy harvesting.

 

Wave propagation in multistable magneto-elastic lattices

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Journal Reference

International Journal of Solids and Structures, Available online 9 December 2014. M. Schaeffer1 , M. Ruzzene1, 2
1 George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 801 Ferst Dr, Atlanta, GA 30332, United States.

2 Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, 270 Ferst Dr, Atlanta, GA 30332, United States.

Abstract

One dimensional (1D) and two dimensional (2D) magneto-elastic lattices are investigated as examples of multistable, periodic structures with adaptive wave propagation properties. Lumped-parameter lattices with embedded permanent magnets are modeled as point magnetic dipole moments, while elastic interactions are described as axial and torsional springs. The equilibrium configurations for the lattices are identified through minimization of the lattice potential energy. Bloch wave analysis is then conducted for small perturbations about stable equilibria to predict corresponding wave propagation properties. Finally, nonlinear dynamic simulations validate the findings of the linearized unit cell analysis, and illustrate the changes in dynamic behavior caused by topological transitions. Case studies for 1D systems show how pass bands and bandgaps are defined by lattice reconfigurations and by changes in lattice magnetization. In 2D systems, hexagonal lattices transition from regular honeycombs to re-entrant ones, which leads to significant changes in wave speeds, and directionality of wave motion and transition fronts.

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