301 citations · 897 across the 43 of their papers we have counts for
7 papers · 1 filter
Axisymmetric deformation of compressible, nearly incompressible, and incompressible thin layers between two rigid surfaces
Alexander B. Movchan, Kirill R. Rebrov, Gregory J. Rodin
Accurate asymptotic solutions are presented for axisymmetric deformation of thin layers constrained by either two rigid plates or two rigid spheres. Those solutions are developed u…
On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions
Vladimir Maz'ya, Alexander Movchan, Michael Nieves
In this paper we consider formal asymptotic algorithms for a class of meso-scale approximations for problems of vibration of elastic membranes, which contain clusters of small iner…
Dynamic interfacial trapping of flexural waves in structured plates
Stewart G. Haslinger, Richard V. Craster, Alexander B. Movchan +2
The paper presents new results on localisation and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particula…
Resonant waves in elastic structured media: dynamic homogenisation versus Green's functions
Alexander Movchan, Leonid Slepyan
We address an important issue of a dynamic homogenisation in vector elasticity for a doubly periodic mass-spring elastic lattice. The notion of logarithmically growing resonant wav…
Corrugation crack front waves
J. R. Willis, N. V. Movchan, A. B. Movchan
The paper presents a model of a dynamic crack with a wavy surface. So far, theoretical analysis of crack front waves has been performed only for in-plane perturbations of the crack…
Uniform asymptotic formulae for Green's functions in singularly perturbed domains
V. Maz'ya, A. Movchan
Asymptotic formulae for Green's functions for the operator $-\GD$ in domains with small holes are obtained. A new feature of these formulae is their uniformity with respect to the…