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SUMMARY:AITKEN PUBLIC LECTURE - Shaken but not stirred: using mathematics 
 in earthquakes - Prof. Hinke Osinga\, University of Auckland
DTSTART:20170510T150000Z
DTEND:20170510T160000Z
UID:TALK72275@talks.cam.ac.uk
CONTACT:Prof. Julia Gog
DESCRIPTION:Earthquakes can cause substantial damage to buildings in ways 
 that are still not well understood. The amplitude and principal frequency 
 of an earthquake are two primary components that affect the extent of the 
 damage\, and they are the basis for many design specification guidelines. 
 We investigate how an external force with varying amplitude and principal 
 frequency affects structural stability. As an example we consider a model 
 of a planar\, post-tensioned frame that exhibits dynamics quite similar to
  the experimental measurements of a scaled model on a shake table. The fra
 me remains structurally sound as long as the tilt angle of the frame does 
 not exceed a certain maximum. Many results in the literature are obtained 
 from performing a large number of simulations over a range of amplitudes a
 nd frequencies. Such a brute-force approach establishes a region in the fr
 equency-amplitude plane for which the structural stability of the frame ev
 entually fails. Our  approach is much more efficient and uses a novel comp
 utational method that approximates the failure boundary directly. This met
 hod is based on continuation of a suitable two-point boundary value proble
 m. Our computations demonstrate that the failure boundary is only piecewis
 e smooth and the results highlight further interesting details of how the 
 dynamics is organised in the frequency-amplitude plane. We find that failu
 re can occur in profoundly different ways\, due to inherent nonlinearities
  in the system. Stability is particularly affected in a nonlinear way if t
 he natural frequency of the structure is close to that of the external for
 cing.\n\nBooking required: https://aitken-damtp.eventbrite.co.uk/\n\nThis 
 talk is part of Prof. Osinga’s tour as the Aitken Lecturer\, which is aw
 arded jointly by the LMS and the NZMS\, more details can be found here: ht
 tps://www.lms.ac.uk/events/lectures/forder-and-aitken-lectureship
LOCATION:MR2\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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