Wave propagation in square granular crystals with spherical interstitial intruders

Abstract

We investigate the propagation and scattering of highly nonlinear waves in granular systems composed of spheres in contact arranged in a square packing, and study how the presence of small and light spherical interstitial defects, also referred to as intruders, affects the wave propagation. The effects of a single defect are investigated experimentally and compared to numerical simulations, showing very good quantitative agreement. Transmitted and scattered waves are formed, whose characteristics depend on the material properties of the defect in relation to the properties of the particles in the lattice. Experiments and numerical simulations reveal that stiffer defects are more efficient at redistributing energy outside the impacted chain and soft defects induce a localization of the energy at the defect. Finally, the effects of the presence of two defects, placed diagonally or aligned in the square packing are also investigated, as well as how their interaction depends on their relative positions.

On the coupling dynamics between thermally stressed beams and granular chains

“…The two-chain arrangement discussed in the previous section may resemble the case of a single chain with an impurity at the middle [16,17,[30][31][32][33][34][35]. Szelengowicz et al [30] summarized the elementary interaction of light or heavy intruders with shock waves.…”

“…Szelengowicz et al [30] summarized the elementary interaction of light or heavy intruders with shock waves. Hascoët and Herrmann [32] showed using numerical simulations that a light defect acts as a secondary source of solitary waves, whereas a heavier defect creates a train of solitary pulses forward and a stable wave backward.…”

Stress Wave Propagation in Two-dimensional Buckyball Lattice

“…1) without any symmetrical or collision mode-related simplifications. It is advantageous over previous numerical methods with respect to calculation precision4647484955. The 2D equation of motion of i th C 60 can be given as…”

“…It makes granular materials a promising candidate for shock disintegration, energy harvesting, nondestructive testing, etc2627282930313233343536373839404142. Wave properties of coherent tightly packed granular systems in 2D and 3D have also been investigated, for example, 2D square packing, curved channel, Y-shaped packing and ordered granular network4344454647484950515253545556575859. Recently, inspired by these macroscopic studies, we have carried out investigations of the counterpart system at nanoscale, and were able to show that 1D arrayed buckyball (C 60 ) system, resembling macroscale spheres, also supports strongly nonlinear Nesterenko solitary wave60.…”

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

“…Wave propagation has been studied extensively in one-dimensional (1D) granular crystals where robust highly localized waves and variants thereof have been identified in various configurations, see the reviews [23][24][25][26]. Higher dimensional granular crystals have also been studied [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], but to a far lesser extent than in 1D. If the particles are packed so that they are just touching, then the resulting dynamics are purely nonlinear, and hence there is no dispersion.…”