Dispersion curves of electromagnetically actuated nonlinear monoatomic and mass-in-mass lattice chains

Abstract Including nonlinearity can lead to fascinating wave propagation behavior in phononic crystals, broadening their possible applications in acoustic engineering. The current work aims to benefit from the exclusive properties of nonlinear chains, on one hand, and electromagnetic actuation, on the other hand, to actively control and deliberately manipulate propagating waves in monoatomic and mass-in-mass chains. First, the governing equations are derived and analytic dispersion relations for the nonlinear propagation of waves are provided using the modified Lindstedt-Poincare method. Then, the effects of electromagnetic actuation on the dispersion curves as well as wave-filtering capabilities of nonlinear lattice chains are investigated. Furthermore, a detailed analysis of the effects of electromagnetic actuation on the stop-bands with local resonance (LR) nature in mass-in-mass chains is performed. The results reveal that successful implementation of the electromagnetic actuation to the studied systems can efficiently manipulate their wave-propagation characteristics, providing about 25% tunability in the stop-band frequency range of monoatomic chains and about 15% in mass-in-mass chains. Also, additional controllable low-frequency stop-bands can be generated as a result of applying electromagnetic actuation leading to higher tunability of wave propagation/attenuation in nonlinear phononic chains.