Interaction of highly nonlinear solitary waves with large plates

Due to geometric nonlinearity, stress waves of one-dimensional granular chains behave as highly nonlinear solitary waves. Those waves can support a high level of amplitude over a long distance and have an important engineering value for detecting structure properties. Deflection can be caused by the impact of a granular bead with large plates. Based on Hertz´s law, using the theory of intrinsic inelasticity to explain the energy loss caused by deflection, we obtain the complete differential equation system of granular chains interacting with structures. By solving the equations, we obtain the displacement solution and velocity solution of beads and find that reflected solitary waves are sensitively affected by the physical properties and thicknesses of the plates.