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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Asymptotic analysis of dynamic problems for elasti
c media with clusters of small inclusions - Michae
l Nieves (Keele University)
DTSTART;TZID=Europe/London:20230323T120000
DTEND;TZID=Europe/London:20230323T123000
UID:TALK195715AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/195715
DESCRIPTION:In this talk\, we discuss an asymptotic approach u
sed to accurately predict the vibration response o
f elastic media containing clusters of many\, smal
l\, closely interacting inclusions of arbitrary sh
ape [1]. The approach is based on the so-called me
thod of mesoscale approximations\, previously deve
loped for quasi-static problems [2]. The resulting
approximations make use of model solutions to dyn
amic problems (i) posed in the medium when the inc
lusions are absent and (ii) involving individual i
nclusions. These model solutions are combined with
appropriate weights that solve a linear algebraic
system\, which naturally appears in attempting to
satisfy the boundary conditions to a high order o
f accuracy and contains information about the size
and shape of each inclusion\, as well as their in
teraction. The method presented yields uniformly a
ccurate approximations for fields associated with
scattering problems and eigenmodes of finite syste
ms containing defect clusters and allows one to (i
) obtain effective models for the cluster at low-f
requencies and (ii) address scenarios involving di
lute clusters. \;The theoretical results are a
ccompanied by numerical illustrations that demonst
rate the effectiveness of the approach.\nReference
s:\n[1] Nieves\, M.J. and Movchan\, A.B. (2022). A
symptotic analysis of in-plane dynamic problems fo
r elastic media with rigid clusters of small inclu
sions. Phil. Trans. R. Soc. A.380: 20210392. doi:
http://doi.org/10.1098/rsta.2021.0392\n[2] Maz'ya
V.G.\, Movchan\, A.B.\, Nieves\, M.J. (2013): Gree
n's Kernels and Meso-Scale Approximations in Perfo
rated Domains\, Lecture Notes in Mathematics\, pp.
XVII\, 258\, Springer Cham. doi: https://doi.org/
10.1007/978-3-319-00357-3
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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