Experimentally observed evolution between dynamic patterns and intrinsic localized modes in a driven nonlinear electrical cyclic lattice

TL;DR

This study experimentally demonstrates how driven nonlinear cyclic electrical lattices can transition between different localized modes, revealing a tunable nonlinear excitation mechanism with potential applications in various nonintegrable systems.

Contribution

It provides the first experimental observation of the continuous transformation between localized lattice modes and intrinsic localized modes in a driven nonlinear electrical lattice.

Findings

LSMs can be tuned across the modal spectrum by adjusting system parameters.

LSMs can be converted into ILMs by tuning the driver frequency.

Impurities influence pattern formation and mode stability.

Abstract

Locked intrinsic localized modes (ILMs) and large amplitude lattice spatial modes (LSMs) have been experimentally measured for a driven 1-D nonlinear cyclic electric transmission line, where the nonlinear element is a saturable capacitor. Depending on the number of cells and electrical lattice damping a LSM of fixed shape can be tuned across the modal spectrum. Interestingly, by tuning the driver frequency away from this spectrum an LSM can be continuously converted into ILMs and visa versa. The differences in pattern formation between simulations and experimental findings are due to a low concentration of impurities. Through this novel nonlinear excitation and switching channel in cyclic lattices either energy balanced or unbalanced LSMs and ILMs may occur. Because of the general nature of these dynamical results for nonintegrable lattices applications are to be expected. The ultimate stability of driven aero machinery containing nonlinear periodic structures may be one example.