A numerical study of the dynamics of the surface grain in a granular chain and the role of gravity
This paper studies the 1-D problem of impulse propagation of mechanical energy through a vertical alignment of spherical grains. The authors focus on the dynamics of the surface top (where the impulse is initiated) as gravity is varied. The grains are assumed to interact via the nonlinear Hertz potential. To make the system representative of effect of large depth where gravitational loading on grains is significant and the non-linear nature of the grain-grain interactions is suppressed, there are studied the systems with up to ten thousand grains. The paper investigates the system for the gravitational acceleration \(g = 0\) and \(g > 0\). The effects of restitutional losses are ignored in this study. The aim is that an understanding of the dynamics of the surface grain alone could reveal the details of impulse propagation and backscattering as it passes through a granular chain and hence could be valuable for test interrogation of these systems. In the \(g = 0\) case, the impulse ends up traveling as a solitary wave which breaks and reforms at collision with a boundary wall and with one another. The surface grain kinetic energy as a function of time is characterized by spikes. The small spikes are due to the formation of secondary solitary waves. After some times, the original pulse is replaced by a dense collection of spikes with different amplitudes depending on the system properties. When \(g > 0\) and a monodisperse chain considered, the backscattered energy received by the surface grain possesses high frequency characteristics and lower frequency envelope oscillations. The analysis of power spectra of the backscattered energy of the surface grain reveals that the overall frequency dependence of the grains has no significant variation with \(g\). In the case of \(g > 0\) and the different grain masses, it is found that the surface grain dynamics becomes noisy. Polydispersity affects the collective vibrations of the grain column. For strong enough polydispersity, the g-dependence of the dynamics of the surface grain is effectively lost.
scientific article; zbMATH DE number 5134114