Details of Grant 

EPSRC Reference:	GR/R05437/01
Title:	Inter-Disciplinary Applications of the Wittrick-Williams Algorithim
Principal Investigator:	Williams, Professor F
Other Investigators:	Howson, Dr W
Researcher Co-Investigators:
Project Partners:	Dalian University of Technology
Department:	Sch of Engineering
Organisation:	Cardiff University
Scheme:	Standard Research (Pre-FEC)
Starts:	01 January 2001	Ends:	31 December 2003	Value (£):	140,017
EPSRC Research Topic Classifications:	Eng. Dynamics & Tribology
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
Problems in many disciplines can be categorised as those which are solved by approximate methods, including commonly used discretisation procedures such as the finite element method, and those which are solved by methods which avoid such approximations by solving the differential equations exactly. Many real life problems also involve eigenvalue problems. Linear eigenvalue problems are the commonest form of eigenproblem but other forms exist. When discretisation errors are avoided by solving appropriate differential equations the eigenvalue problem is a transcendental one, ie the elements of the matrix are transcendental functions of the eigenparameter. In structural analysis vibration problems the frequency of vibration is the eigenparameter and the natural frequencies are the eigenvalues. The Wittrick-Williams algorithm was developed in 1970 to obtain eigenvalues with certainty and is still the only method giving certainty for structural transcendetal eigenvalue solutions. The present project explores the extent to which the Wittrick-Williams technology can be transferred to other disciplines by checking whether problems in those disciplines satisfy both of the requirements that: a discretised solution would give an eigenvalue problem with a Sturm sequence property and; it is possible to alternatively set up and solve appropriate differential equations. Areas expected to yield technology transfer include the H( control state feedback problem and precise solutions for surface wave propagation in stratified material.
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