Tunable topological interface states in one-dimensional extended granular crystals

Abstract

This paper theoretically and numerically investigates a topological interface state in a highly tunable granular crystal. This system allows us to tune the contact stiffness in a controllable manner, via altering the precompression between the spheres. The spatial change of particles contact stiffness results in band inversion and topological phase transition in the first kind of sub-lattice, which requires a linear and Hertzian contacts stiffness corresponding to the two interface interactions between particles in one unit cell. The second kind of sub-lattice only composed of particles is developed, of which topological state is not adjusted during the pre-compressed process. Therefore, a one-dimensional extended granular crystal is established by placing adjacently two different sub-lattices. Furthermore, we analytically and computationally consider the frequency response of this periodic structure, and further predict the existence of a tuning-frequency topologically interface mode. Finally, this phenomenon is confirmed through employing the transient response analysis calculated by the state space method and the finite element numerical approach.