Wave self-interactions in continuum phononic materials with periodic contact nonlinearity

Abstract

The existence of nonlinearity within materials manifests richer wave propagation compared to their linear counterpart in the form of amplitude-dependent material response and energy transfer between frequencies. While these properties have been extensively studied in the case of continuous and discrete nonlinear phononic materials (PMs), individually, the behavior of continuum PMs with discrete nonlinearities, which could open new opportunities for wave propagation control via discrete–continuum coupling, is relatively unexplored. In this article, we investigate nonlinear wave propagation through one-dimensional continuum PMs with periodic contacts. Specifically, the periodicity is in the form of pre-compressed rough contacts resulting in nonlinearly coupled linear finite thickness elastic layers. We analyze the system using full-scale time-domain finite element simulations by treating the contacts as spring-equivalent nonlinear thin elastic layers. The model considers a power-law pressure-gap relationship at the rough contacts. The evolution of propagating nonlinear waves within the weakly nonlinear regime is illustrated, emphasizing the generation of zero (DC), self-demodulated low, and second harmonic frequencies for excitation in different zones of the dispersion relation. The continuum between discrete contact nonlinearities exhibits local DC reduction and second harmonic increment, not observed in discrete PMs such as granular phononic crystals. The intertwined effects of nonlinearity, periodicity, and finiteness on nonlinear wave propagation are also explored, which results in maximum DC amplitude at the finite boundaries of the PMs and mode-based second harmonic characteristics. Finally, we demonstrate the flexibility of the proposed nonlinear PMs by characterizing the dependence of nonlinear wave propagation on different arrangements of embedded contacts. The concept of discretely embedding nonlinear interfaces, such as rough contacts, within an elastic continuum, opens opportunities to control the global nonlinear response of the PMs through local microstructural nonlinearities.