Universal design law of equivalent systems for Nesterenko solitary waves transmission

Wave propagation behavior within 1D granular chain has been a much-studied topic in the past decades due to its novel physical wave phenomena. The initial motivation of the present study was prompted by how to construct a granular system with desired wave properties and particle motions. Here, we systematically report the methodology to construct equivalent systems (systems with identical output) using theoretical analysis, experiments and numerical simulation. We investigate the properties of Nesterenko solitary wave supported by one-dimensional granular chains and achieve an equivalent wave transmission among various materials and dimensions. The results of typical experiments and finite element analysis fully support the established theoretical predictions based on Hertz contact and long wavelength approximation theory, which yields a broad class of equivalent systems. Finally, an instructive mechanism map, containing various equivalent systems, is proposed to clarify the relationship between geometric parameters and material properties, providing insights into designing a desired nonlinear dynamic system and guidance for potential engineering applications.