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Evolution and collision of wave fronts in two-dimensional hexagonal packing granular lattices

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Abstract

In this paper, we investigate evolution and collision of wave fronts propagating in two-dimensional (2D) hexagonal packing confined in a rectangular region, using the fifth-order Runge–Kutta numerical scheme, under various impacts including one impact, continuous impacts and discontinuous impacts. For the case of one impact, numerical results indicate that the phase of the wave front is not in phase and the relationship between the peak amplitude of the velocity \({V}_{max}\) and the distance \(m\) from the center of the wave front satisfies the equation \({V}_{max}\sim exp(dm)\). With the increase of propagating depth, the attenuation of velocity at each position of the wave front is also different. At the corner of the wave front moving in the y-direction, the peak amplitude of velocity follows the exponential relationship with the depth, which can be described by the nonlinear mapping method. But at the center, the peak amplitude no longer strictly follows the exponential relationship with the depth. For the case of continuous impacts, the decay of the peak amplitude is slower than that of one impact. Numerical simulations indicate that independent wave fronts induced by two discontinuous impacts, may merge in to one after a certain depth. The center of the merged wave front is moved to a new position, the peak amplitude at the center of the merged wave front also follows the exponential decay with the depth. When impacts are periodically distributed, our numerical results confirm that the wave fronts eventually evolve into a uniform wave front that can well be described by Nesterenko’s continuum approximation of a 1D chain of spheres. Our results provide a new idea for generating a plane wave front and effectively avoid the influence of defects or impurities.

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Funding

This research is supported in part by the National Natural Science Foundation of China (Grant Nos. 11774417) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20160238).

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  1. School of Material Science and Physics, China University of Mining and Technology, Xuzhou, 221116, China

    Yang Xian-qing, Meng Xian-wen & Zhang Wei

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  1. Yang Xian-qing
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  2. Meng Xian-wen
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  3. Zhang Wei
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Correspondence to Yang Xian-qing.

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Xian-qing, Y., Xian-wen, M. & Wei, Z. Evolution and collision of wave fronts in two-dimensional hexagonal packing granular lattices. Granular Matter 24, 88 (2022). https://doi.org/10.1007/s10035-022-01246-2

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