Nonlinear elastic waves in a chain type of metastructure: theoretical analysis and parametric optimization

Nonlinear elastic wave propagations in metamaterials and metastructures exhibit much richer dynamic behaviors in comparison with the linear cases. This paper studies the generation of superharmonic wave in a chain type of multi-cell aperiodic structure with nonlinear stiffness. An analytical approach, integrated with the first-order perturbation method and the harmonic balance method, is developed to describe nonlinear wave response with spectrum of higher-order harmonics. The cubic nonlinearity brings the amplitude-dependent bandgap and the nonreciprocal wave phenomenon with the combination of aperiodicity in arrangement, which are presented via both analytical approach and numerical computation. Further, the study introduces a new strategy of parametric optimization on the distribution of multiple local resonances, based on the genetic algorithm method. The optimized metastructures exhibit noteworthy wave properties, including the broadband nonlinear wave suppression, the tunability of wave attenuation on transmissibility level, and the unidirectional wave transmission, by designing different optimization functions in the developed optimization scheme. This work provides an idea to elucidate nonlinear wave responses caused by nonlinear stiffness and to explore wave properties via parametric optimization.