Nonlinear wave scattering at the interface of granular dimer chains and an elastically supported membrane

In this work we study computationally nonlinear wave scattering at the flexible interfaces of 1D dimer granular chains with a square membrane with a linear uniform elastic foundation. A computational algorithm that combines successive iterations and interpolations is developed to accurately model the highly nonlinear and non-smooth scattering of impeding pulses from the granular chains to the flexible boundary. Energy localization (through the excitation of local transient breathers), intense wave transmission or reflection, as well as strong pulse scattering in the frequency/wavenumber domain are detected for varying mass ratios of the dimers and stiffness of the elastic foundation of the membrane. Moreover, it is found that the realization of resonances or anti-resonances in the dimer granular chains at different mass ratios has significant effects on the nonlinear wave scattering at the flexible boundary. Interestingly enough, an inverse relation between the foundation stiffness and the residual energy transferred to the membrane from the impulsively excited dimer is found. Finally, we show that the energy exchanges between two granular chains interacting through the flexible foundation strongly depend on the distance between them. The presented results and the associated computational method discussed in this work contribute to the predictive modeling and design of granular media with flexible interfaces.