A mapping discrete element method for nonlinear dynamics of vibrating plate-particle coupling system

Abstract

A mapping discrete element method is presented to study dynamic behaviors of the vibrating plate-particle coupling system. The continuum is partitioned into a mesh of mass points and simulated by the discrete element method, where the mass, stiffness and damping is mapped from the global mass, stiffness and Rayleigh damping matrix in the finite element method. The coupling between the continuum and the discrete particle material is realized by expanding the surface mass points into spheres. Therefore, the continuum's internal force and deformation can be accurately calculated whilst using the efficient spherical contact detection to couple and interact with particles. In the vibrating plate-particle system, the non-linear phenomena observed during the experiment are further studied by the proposed method. The results show that the velocity distribution of the particle system changes significantly when the jump phenomenon occurs, and the disruption of the uniform motion of the particle system by the vibrating plate is one of the key factors that creates the jump phenomenon. Furthermore, it is noticed in the simulation that the movement of particles above the plate is similar to bouncing ball causing frequency and period doubling phenomenon. Moreover, a linear region is found in the low frequency band, where the particles additional effects on the mass and stiffness of the plate are evident and the excitation amplitude has a lesser effect on power dissipation compared to other frequency bands.