Details of Grant 

EPSRC Reference:	GR/J97465/01
Title:	MODAL INTERACTION AND NONLINEAR VIBRATIONS IN SHELL STRUCTURES
Principal Investigator:	Thompson, Professor J
Other Investigators:	Croll, Professor JGA McRobie, Professor A
Researcher Co-Investigators:
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Department:	Civil Environmental and Geomatic Eng
Organisation:	UCL
Scheme:	Standard Research (Pre-FEC)
Starts:	15 November 1994	Ends:	14 April 1998	Value (£):	118,596
EPSRC Research Topic Classifications:	Continuum Mechanics
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Summary on Grant Application Form
We propose to study the physics of the dynamic stability and modal interaction in the nonlinear vibrations of shell structures using modern methods developed primarily for fluid mechanics; in particular the inertial manifolds and their approximation by finite element methods. Not only is the understanding of the dynamical behaviour of shell structures important in its own right, but shells provide an ideal test-ground for the development of appropriate methods for the analysis of modal interaction in weakly nonlinear systems:- in engineering terms, the transfer of energy between modes. Although the literature on the perturbation methods for the analysis of this phenomenon is large, there is much scope for this work to be reconsidered in a more coherent mathematical framework. We propose to use a top-of-the-range finite element package for computing eigenvalues and eigenvectors and for nonlinear, time history simulations of shell dynamics, for some particular case-studies. These results may then be compared with existing perturbation methods. The aim of the project is to unify these disparate approaches and develop improved methods for understanding both the physics and the numerics. In particular we wish to discover i) what are the mechanics of energy transfer between modes; ii) how does the interaction between buckling and vibration modes affect the dynamic stability and iii) is there a sensible dimension-reduction algorithm for high dimensional finite element models similar to component mode synthesis, but capable of dealing with distributed nonlinearities?
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