Hutzler S, Ryan-Purcell J, Mughal A, Weaire D
School of Physics, Trinity College Dublin, The University of Dublin, Dublin, Republic of Ireland.
Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, Wales SY23 3BZ, UK.
R Soc Open Sci. 2023 Jul 12;10(7):230293. doi: 10.1098/rsos.230293. eCollection 2023 Jul.
A line of contacting hard spheres, placed in a transverse confining potential, buckles under compression or when tilted away from the horizontal, once a critical tilt angle is exceeded. This interesting nonlinear problem is enriched by the combined application of both compression and tilt. In a continuous formulation, the profile of transverse sphere displacement is well described by numerical solutions of a second-order differential equation (provided that buckling is not of large amplitude). Here we provide a detailed discussion of these solutions, which are approximated by analytic expressions in terms of Jacobi, Whittaker and Airy functions. The analysis in terms of Whittaker functions yields an exact result for the critical tilt for buckling without compression.
一排紧密接触的硬球，置于横向约束势中，一旦超过临界倾斜角，在压缩时或从水平方向倾斜时就会发生屈曲。压缩和倾斜的联合应用使这个有趣的非线性问题更加丰富。在连续表述中，横向球位移的轮廓可以通过二阶微分方程的数值解很好地描述（前提是屈曲幅度不大）。在这里，我们详细讨论这些解，它们可以用雅可比函数、惠特克函数和艾里函数的解析表达式来近似。用惠特克函数进行的分析得出了无压缩时屈曲的临界倾斜的精确结果。
