- Open Access
Meta-atom based two-sphere Newton's cradle
Phys. Rev. E 112, 035506 – Published 25 September, 2025
DOI: https://doi.org/10.1103/2whk-jc4b
Abstract
Locally resonant metamaterials are among the most studied types of elastic and acoustic metamaterials, with significant research focused on wave propagation in a periodic array of “meta-atoms.” Here we investigate the collision dynamics of two identical pendulum-suspended mass-in-mass resonators, essentially a two-sphere Newton's cradle, emphasizing the readily realizable scenario where the internal resonator frequency is much greater than the pendulum frequency. We first show that the dynamics of a collision can be described using effective parameters, similar to how previous metamaterials research has characterized wave propagation through effective material parameters. Nonconventional collision dynamics—observed in two colliding mass-in-mass systems where one is initially at rest—include behaviors such as the moving sphere rebounding as if from a fixed wall while the other remains essentially stationary, the spheres coupling and moving forward in near-unison, and the spheres recoiling in opposite directions. These responses can be achieved by tuning the effective parameters. We demonstrate that these parameters can take on values that differ significantly from those in a conventional Newton's cradle. Additionally, we investigate multiple collisions of the two spheres, revealing complex dynamics. This work paves the way for the development and study of new “collision-based metamaterial” structures.
Physics Subject Headings (PhySH)
Corrections
2 October, 2025
Correction: A typographical error in the first sentence of the abstract has been fixed.
Article Text
Supplemental Material
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- See Supplemental Material at http://link.aps.org/supplemental/10.1103/2whk-jc4b for the derivation of the pendulum dynamics of the two-sphere mass-in-mass Newton's cradle; derivation of the instantaneous effective coefficients of restitution and motion ; derivation of the postcollision velocity in the external potential; derivation of the overall effective coefficient of restitution and effective coefficient of motion for the average postcollision motion; density plots for the initial velocities of each spherical shell in the external potential after impact; and the animations of the simulated motion of the dynamics of the system for several different values of the resonator parameters and precollision energy.
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