On the signature of nonlinearity in the wave characteristics of anharmonic chains
Ganesh Ramakrishnan (University of Minnesota), Stefano Gonella (University of Minnesota)
Joint session: Mechanics and Dynamics of Periodic Structures and Dynamic Behavior of Materials
Tue 4:20 - 5:40
Salomon 101
Nonlinear phononic crystals present themselves as flexible mechanical filters due to the inherent tunability of their propagation and attenuation zones. The motive of this work is to understand the wavefield characteristics that are responsible for this nonlinearity-induced band gap modulation. This objective is achieved by monitoring the spatial and spectral features of the wave event triggered in the chain by the excitation with narrow-band bursts. Specifically, a monoatomic chain with quadratic nonlinear springs is considered as the benchmark system for this study. Perturbation techniques suggest that the cutoff frequency for wave propagation is not significantly altered by the presence of nonlinearity. However, the spatiotemporal response features show interesting deviations from the case of a corresponding linear chain. Through the inspection of the contours of the spectral response, it is concluded that the nonlinear wave behavior can be represented as the modulation of the inherent linear response by means of a sigmoidal long-wavelength component. Furthermore, it is seen that a parameterization of the sigmoidal profile gives rise to an inverse problem which can be used to determine the magnitude of the nonlinear term in the constitutive model. The applicability of this technique is demonstrated for a system of spheres in contact governed by different hypothetical power laws. Finally, an attempt is made to understand the shock-like feature of the sigmoidal profile by studying the long-wavelength approximation of the quadratic nonlinear chain.