Wavenumber Scattering and Inter-band Targeted Energy Transfer in Phononic Lattices with Local Vibro-Impact Nonlinearities

TL;DR

This paper introduces a novel method using local vibro-impact nonlinearities to control wave scattering and energy transfer across bands in phononic lattices, enabling targeted manipulation of wave energy distribution.

Contribution

The study demonstrates non-resonant energy scattering and inter-band targeted energy transfer in phononic lattices with vibro-impact nonlinearities, supported by computational and reduced order model analysis.

Findings

Energy scattering depends on wave energy in 1D lattice.

Inter-band energy transfer scales with input energy.

ROM analysis reveals resonance conditions matching energy transfer behavior.

Abstract

We propose a method for manipulating wave propagation in phononic lattices by employing local vibro-impact (VI) nonlinearities to \textit{scatter} energy across the underling linear band structure of the lattice, and \textit{transfer} energy from lower to higher optical bands.Inspired by recent developments in the field of nonlinear targeted energy transfer (TET) using \textit{non-resonant} energy exchanges, we achieve this using spatially localized VI forces that redistribute energy across the linear spectrum of the lattice in a non-resonant fashion.First, a 1-dimensional (1D), 2-band phononic lattice with embedded VI unit cells is computationally studied to demonstrate that energy is scattered in the wavenumber domain, and this nonlinear scattering mechanism depends on the energy of the propagating wave. Next, a 4-band lattice is studied with a similar technique to demonstrate the concept of inter-band targeted energy transfer (IBTET) and to establish analogous scaling relations with respect to energy. To interpret the results of IBTET, we study the nonlinear normal modes (NNMs) of a reduced order model (ROM) of the VI unit cell in the 4-band lattice, using the method of numerical continuation. Interestingly, the slope of the frequency-energy branches of the ROM corresponding to the 1:1 resonance NNM matches remarkably well with the dependence of IBTET to input energy in the 4-band lattice. Moreover, relations between the dynamics of the VI lattice and the NNMs of the underlying Hamiltonian system provide physical interpretations for the relative energy transfers.