Time-Dependent Nonlinear Metamaterial: A Circular Inclusion for Harmonic Manipulation

This study explores the dynamic scattering behavior of nonlinear bulk ultrasonic waves interacting with time-dependent nonlinear inclusions. By assuming time-varying third-order elastic constants in the Murnaghan constitutive framework, we model the local resonances within 2D circular nonlinear inclusions embedded in a linear matrix. This approach introduces new challenges in understanding harmonic scattering, as theoretical analysis becomes intricate. Finite element simulations are employed to investigate the dynamics of harmonic wave scattering from a single, time-evolving circular nonlinear inclusion.

When a monochromatic longitudinal wave interacts with this time-dependent circular inclusion, harmonic scattering emerges, accompanied by an exchange of higher harmonic energy between longitudinal and transverse modes at varying scattering angles. The relationship between the input pulse frequency and the dynamic frequency of the inclusion reveals the generation of both integer and fractional harmonic components in the scattered waves.

This study suggests that time-dependent nonlinear inclusions hold potential for developing innovative mechanical metamaterials with controlled harmonic behavior, unlocking new functionalities and design possibilities.