Minimal model of a linear granular chain bouncing against a vibrating plane. Chi-Hang, Ng ^{1,2*}, Tsai, JC^{2}, Jung-Ren, Huang^{2}^{1}Department of Physics, National Taiwan University, Taipei, Taiwan^{2}Institute of Physics, Academia Sinica, Nankang, Taiwan* presenting author:Jack Ng, email:cckhunter@gmail.com We simulate a granular chain bouncing against a horizontal plane undergoing a vertical sinusoidal oscillation. The model chain consists of linearly connected particles with dissipative internal forces proportional to the velocity difference of the neighboring particles. For the sake of simplicity, we only consider the vertical motions of the chain particles. The simulation results show that the chain profile can be categorized with three modes: flat, one-end, and both-end curve-up. All three modes are linear combinations of the normal modes of lowest few nodes of the model. The long-time dynamics of chain bouncing can be understood as the transitions between these modes. The detailed short-time analysis of the chain profile suggests that the transitions are triggered by the asymmetric velocities of the end particles right after bouncing.
Keywords: Numerical simulation, granular particle, chain model |