Amplitude-activated mechanical wave manipulation devices using nonlinear metamaterials

Abstract

We report device implications for acoustic metamaterials with various nonlinear oscillator microstructures as passive amplitude-activated mechanical wave filters and waveguides using simulations on their representative one-dimensional discrete element models. Linear and various nonlinear hardening and softening stiffness cases and combinations thereof are considered for the local oscillators. The propagation and attenuation characteristics of harmonic waves in a tunable frequency range are found to correspond to the excitation amplitude and nonlinearity-dependent shifts in the local resonance bandgap for such nonlinear acoustic metamaterials. Three passive acoustic devices—(i) amplitude-activated selective filter, (ii) amplitude band pass or band rejection filter, and (iii) direction-biased waveguide—are demonstrated numerically. Constituent frequency components in bifrequency excitations are shown to be retained or diminished to varying degrees within acoustic metamaterials with either hardening or softening local oscillators depending on their individual amplitudes. Using trilinear hardening or softening oscillators instead switches the response between attenuation and propagation respectively, outside of a tunable bandwidth of amplitude for the same excitation frequency. Whereas, amplitude-dependent, passive direction-bias in propagation characteristics for a given excitation frequency is demonstrated in a metamaterial waveguide composed of units with tuned combinations of linear and nonlinear hardening oscillators deployed in sequence. These predictions indicate the possibility of realizing acoustic metamaterials having passive adaptive, amplitude-activated dynamics using tailored combinations of nonlinear oscillators to elicit prescribed wave transformations across them.