TY - JOUR
T1 - Wave self-interactions in continuum phononic materials with periodic contact nonlinearity
AU - Patil, Ganesh U.
AU - Matlack, Kathryn H.
N1 - Funding Information:
This work was supported by the Army Research Office, USA and was accomplished under Grant Number W911NF-20-1-0250 . The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/9
Y1 - 2021/9
N2 - 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.
AB - 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.
KW - Contact nonlinearity
KW - DC component
KW - Nonlinear waves
KW - Phononic materials
KW - Second harmonic generation
KW - Self-demodulation
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U2 - 10.1016/j.wavemoti.2021.102763
DO - 10.1016/j.wavemoti.2021.102763
M3 - Article
AN - SCOPUS:85107065036
VL - 105
JO - Wave Motion
JF - Wave Motion
SN - 0165-2125
M1 - 102763
ER -