# Doubly-nonlinear waveguides with self-switching functionality selection capabilities

## TL;DR

This paper explores how combined quadratic and cubic nonlinearities in doubly-nonlinear waveguides enable tunable elastic wave control, acting as internal switches for high-frequency response features.

## Contribution

It introduces a novel framework analyzing the interplay of two nonlinearities in elastic waveguides, revealing new wave control strategies and design principles for tunable metamaterials.

## Key findings

- Cubic nonlinearity can act as an internal switch for wave modes.
- Interplay of nonlinearities modifies dynamic response signatures.
- Demonstrated control of high-frequency features via nonlinearity tuning.

## Abstract

In this article, we investigate the effects of the interplay between quadratic and cubic nonlinearities on the propagation of elastic waves in periodic waveguides. Through this framework, we unveil an array of wave control strategies that are intrinsically available in the response of doubly-nonlinear systems and we infer some basic design principles for tunable elastic metamaterials. The objective is to simultaneously account for two sources of nonlinearity that are responsible for distinct and complementary phenomena and whose effects are therefore typically discussed separately in the literature. Our study explicitly targets the intertwined effects that the two types of nonlinearity exert on each other, which modify the way in which their respective signatures are observed in the dynamic response. Through two illustrative examples we show how the dispersion correction caused by cubic nonlinearity can be used as an internal switch, or mode selector, capable of tuning on/off certain high-frequency response features that are generated through quadratic mechanisms.