The effect of topological disorder on the dynamic behaviour of topologically constrained oscillator chains is investigated through a normal mode analysis. A measure for mode localization based on the skewness of the density of energy states of normal modes is proposed, which correlates well with main configuration characteristics. Appropriate configuration sampling is achieved by employing the Ising model together with the Metropolis algorithm.
CarcaterraAdell’IsolaFEspositoR, et al. Macroscopic description of microscopically strongly inhomogenous systems: a mathematical basis for the synthesis of higher gradients metamaterials. Arch Ration Mech An2015; 218(3): 1239–1262.
2.
dell’IsolaFSteigmannDCorteAD. Synthesis of fibrous complex structures: designing microstructure to deliver targeted macroscale response. Appl Mech Rev2016; 67(6): 060804.
3.
TurcoERizziNL. Pantographic structures presenting statistically distributed defects: numerical investigations of the effects on deformation fields. Mech Res Commun2016; 100(77): 65–69.
4.
TurcoEGiorgioIMisraA, et al. King post truss as a motif for internal structure of (meta)material with controlled elastic properties. Roy Soc Open Sci2022; 4(10): 171153.
HoriJAsahiT. On the vibration of disordered linear lattice. Prog Theor Phys1957; 17(4): 523–542.
7.
DombCMaradudinAAMontrollEW, et al. Vibration frequency spectra of disordered lattices. I. Moments of the spectra for disordered linear chains. Phys Rev1959; 115: 18–24, https://link.aps.org/doi/10.1103/PhysRev.115.18
8.
DombCMaradudinAAMontrollEW, et al. Vibration frequency spectra of disordered lattices. II. Spectra of disordered one-dimensional lattices. Phys Rev1959; 115: 24–36, https://link.aps.org/doi/10.1103/PhysRev.115.24
HehlenBRuffléB., Atomic vibrations in glasses. In: RichetP (ed.) Encyclopedia of Glass Science, Technology, History, and Culture. Wiley, 2021.
17.
KokoskaSZwillingerD. CRC standard probability and statistics tables and formulae, student edition. Boca Raton, FL: CRC Press, 2000.
18.
MühlichUBallaniFStoyanD. Influence of randomness in topology, geometry and material properties on the mechanical response of elastic central-force networks. Probabilist Eng Mech2015; 40: 36–41.
19.
GulminelliFCarmonaJMChomazP, et al. Transient backbending behavior in the Ising model with fixed magnetization. Phys Rev E2003; 68: 026119.
20.
CarmonaJRichertJTaranconA. A model for nuclear matter fragmentation: phase diagram and cluster distributions. Nucl Phys A1998; 643: 115–134.