Collision of one-dimensional nonlinear chains

Abstract

We investigate one-dimensional collisions of unharmonic chains and a rigid wall. We find that the coefficient of restitution (COR) is strongly dependent on the velocity of colliding chains and has a minimum value at a certain velocity. The relationship between COR and collision velocity is derived for low-velocity collisions using perturbation methods. We found that the velocity dependence is characterized by the exponent of the lowest unharmonic term of interparticle potential energy.

Rupture and recoil of bent-core liquid crystal filaments

“…Dynamic buckling and recoil mechanisms of elastic materials have been studied in materials ranging from solids 1 to rubbers 2 and even to non-Newtonian fluids. [3][4][5][6][7][8] When the axial compression of a straight beam exceeds a critical value, a dynamic buckling instability initiates -as noted first by Euler 9 -with a characteristic wavelength. 1,10,11 The threshold character of this phenomenon may be the first practical example of a critical bifurcation of the solution of a differential equation.…”

Erratum to: Nonsmooth Mechanics

“…However the results in [27,Figure 2a] show that with equal masses and equal stiffnesses, then e n ≈ 1. This is extended to N -ball systems (see also [28,29]). One assumption that is made in these studies, and might make the analysed chains behaviour different from an elastic rod impacting axially a wall, is that it is assumed that the first (colliding) ball reverses its velocity instantaneously [29].…”

“…• Pages 165-166: estimations of the CoR for harmonic chains of aligned beads colliding a wall, and taking into account sequences of repeated impacts as well as the vibrational energy trapped in the chain, are given in [28,29].…”

The unexpectedly small coefficient of restitution of a two-degree-of-freedom mass-spring system and its implications

“…This "loss" approaches zero when the length of chain increases. Nagahiro and Hayakawa [21] further indicated that COR would be velocity dependent if the springs are nonlinear.…”