This project involves the analysis of finite and semi-infinite defects in elastic lattice systems. These defects may be dislocations or variations in inertial properties and, for finite defects, will have an associated spectrum of eigenstates. The focus of the research programme is on the analysis of these eigenstates and the fields in the vicinity of the defect sites; algorithms will be developed to study the solutions in various asymptotic regimes. The research programme will involve both analytical and numerical models. The project may also include the study of edge and interfacial waves in mechanical lattices.
Colquitt DJ, Nieves MJ, Jones IS, Movchan AB, Movchan NV. 2013 Localisation for a line defect in an infinite square lattice. Proc. R Soc. A 469 : 20120579. (doi: 10.1098/rspa.2012.0579)
Colquitt DJ, Nieves MJ, Jones IS, Movchan NV, Movchan AB. 2012 Trapping of a crack advancing through an elastic lattice.
Int J Eng Sci 61, 129–141. (doi: 10.1016/j.ijengsci.2012.06.016)
Madine KH, Colquitt DJ. 2021 Dynamic Green's functions in discrete flexural systems. Q J Mech Appl Math, hbab006. (doi: 10.1093/qjmam/hbab006)