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CATEGORIES:CMS Special Lectures
SUMMARY:AITKEN PUBLIC LECTURE - Shaken but not stirred: us
ing mathematics in earthquakes - Prof. Hinke Osing
a\, University of Auckland
DTSTART;TZID=Europe/London:20170510T160000
DTEND;TZID=Europe/London:20170510T170000
UID:TALK72275AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72275
DESCRIPTION:Earthquakes can cause substantial damage to buildi
ngs in ways that are still not well understood. Th
e amplitude and principal frequency of an earthqua
ke are two primary components that affect the exte
nt of the damage\, and they are the basis for many
design specification guidelines. We investigate h
ow an external force with varying amplitude and pr
incipal frequency affects structural stability. As
an example we consider a model of a planar\, post
-tensioned frame that exhibits dynamics quite simi
lar to the experimental measurements of a scaled m
odel on a shake table. The frame remains structura
lly sound as long as the tilt angle of the frame d
oes not exceed a certain maximum. Many results in
the literature are obtained from performing a larg
e number of simulations over a range of amplitudes
and frequencies. Such a brute-force approach esta
blishes a region in the frequency-amplitude plane
for which the structural stability of the frame ev
entually fails. Our approach is much more efficie
nt and uses a novel computational method that appr
oximates the failure boundary directly. This metho
d is based on continuation of a suitable two-point
boundary value problem. Our computations demonstr
ate that the failure boundary is only piecewise sm
ooth and the results highlight further interesting
details of how the dynamics is organised in the f
requency-amplitude plane. We find that failure can
occur in profoundly different ways\, due to inher
ent nonlinearities in the system. Stability is par
ticularly affected in a nonlinear way if the natur
al frequency of the structure is close to that of
the external forcing.\n\nBooking required: https:/
/aitken-damtp.eventbrite.co.uk/\n\nThis talk is pa
rt of Prof. Osinga’s tour as the Aitken Lecturer\,
which is awarded jointly by the LMS and the NZMS\
, more details can be found here: https://www.lms.
ac.uk/events/lectures/forder-and-aitken-lectureshi
p
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge
CONTACT:Prof. Julia Gog
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