| EPSRC Reference: |
GR/R05406/01 |
| Title: |
Mode Finding When Using the Wittrick-Williams Algorithm, Via Linear Eigensolution Analogy |
| Principal Investigator: |
Williams, Professor F |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Sch of Engineering |
| Organisation: |
Cardiff University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
11 January 2001 |
Ends: |
10 January 2004 |
Value (£): |
140,229
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| EPSRC Research Topic Classifications: |
| Eng. Dynamics & Tribology |
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| EPSRC Industrial Sector Classifications: |
| Aerospace, Defence and Marine |
Construction |
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| Related Grants: |
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| Panel History: |
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Summary on Grant Application Form |
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The problem of finding the natural frequencies of free vibration of structures and the modes (ie shapes) with which they vibrate is of great practical importance, as also is the related problem of finding the load factors and associated modes for which structures buckle. The traditional finite element method is extremely powerful for solving both of these problems by solving a linear eigenvalue problem for which the eigenvalues are the natural frequencies of load factors and the eigenvectors are the modes. Such finite element methods give approximate results due to discretisation errors, such that more expensive solutions using a greater number of elements give better approximations. For a significant range of problems, including frameworks and prismatic assemblies of plates such as used in wings of aircraft it is possible to avoid the discretisation errors by solving appropriate differential equations for the component parts of the structure and hence setting up a stiffness matrix for the entire structure which is a transcendental function of the eigenparameter. The eigenvalues of this transcendental eigenproblem can be extracted with certainty and to any required accuracy by using the Wittrick-Williams algorithm, but the accuracy of the modes found by existing methods is considerably less than for the eigenvalues and is not easy to predict. Ana analogy is established between a hypothetical finite element solution involving an infinite number of degrees of freedom, and hence giving a linear eigenproblem of infinite size, and the transcendental eigenproblem. This is used to enable the extent to which the many excellent solution methods for the linear eigenvalue problem an be successfully adapted to give identical results for the transcendental eigenproblem as would be given by the hypothetical infinite order linear eigenproblem. The transcendental eigensolution methods thus derived are compared and used to obtain very accurate modes and rapid convergence on the eigenvalues for the transcendental eigenproblem.
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Key Findings |
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.cf.ac.uk |