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Interpolation of Mode Shapes: A Matrix Scheme Using Two-Way Spline Curves

Published online by Cambridge University Press:  07 June 2016

G. T. S. Done
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Summary

A method of interpolating low aspect ratio lifting surface mode deflections for use in aeroelastic calculations is described. It is based on the spline curve, the numerical analogue of the draughtsman’s spline which is a thin flexible beam used for drawing a smooth curve through a set of given coordinate points. The present problem is one of surface fitting and a matrix scheme using two-way spline curves is adopted. The method of treating the case in which the data points are randomly placed, whilst retaining an exact fit at the points, is discussed, as are the results of a practical example.

Type
Research Article
Information
Aeronautical Quarterly , Volume 16 , Issue 4 , November 1965 , pp. 333 - 349
Copyright
Copyright © Royal Aeronautical Society. 1965

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References

1. Hitch, H. P. Y. Modern Methods of Investigating Flutter and Vibration. Journal of the Royal Aeronautical Society, Vol. 68, p. 357, 1964.Google Scholar
2. Cadwell, J. H. A Least Squares Surface Fitting Program. The Computer Journal, Vol. 3, p. 266, 1961.CrossRefGoogle Scholar
3. Schoenberg, I. J. Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions. Quarterly of Applied Mathematics, Vol. 4, p. 45 and p. 112, 1946.CrossRefGoogle Scholar
4. Schoenberg, I. J. and Whitney, Anne. On Polya Frequency Functions. Part III: The Positivity of Translation Determinants with an Application to the Interpolation Problem by Spline Curves. Transactions of the American Mathematical Society, Vol. 74, p. 246, 1953.Google Scholar
5. Schoenberg, I. J. Spline Functions, Convex Curves and Mechanical Quadrature. Bulletin of the American Mathematical Society, Vol. 64, p. 352, 1958.CrossRefGoogle Scholar
6. Johnson, R. S. On Mono-Splines of Least Deviation. Transactions of the American Mathematical Society, Vol. 96, p. 458, 1960.Google Scholar
7. Walsh, J. L., Ahlberg, J. H. and Nilson, E. N. Best Approximation Properties of the Spline Fit. Journal of Mathematics and Mechanics, Vol. 11, p. 225, 1962.Google Scholar
8. Ahlberg, J. H. and Nilson, E. N. Convergence Properties of the Spline Fit. Journal of Industrial and Applied Mathematics, Vol. 11, p. 95, 1963.Google Scholar
9. De Boor, C. Best Approximation Properties of Spline Functions of Odd Degree. Journal of Mathematics and Mechanics, Vol. 12, p. 747, 1963.Google Scholar
10. Theilheimer, F. and Starkweather, W. The Fairing of Ship Lines on a High Speed Computer. Mathematics of Computation, Vol. 15, p. 338, 1961.Google Scholar
11. Asker, B. The Spline Curve–a Smooth Interpolating Function used in Numerical Design of Ship-Lines. B.I.T. (see Nordisk Tidskrift Informationsbehandling), Vol. 2, p. 76, 1962.Google Scholar
12. Birkhoff, G. and Garabedian, H. L. Smooth Surface Interpolation. Journal of Mathematics and Physics, Vol. 39, p. 258, 1960.CrossRefGoogle Scholar
13. De Boor, C. Bicubic Spline Interpolation. Journal of Mathematics and Physics, Vol. 41, p. 212, 1962.CrossRefGoogle Scholar
14. Holladay, J. C. A Smoothest Curve Approximation. Mathematical Tables and Other Aids to Computation, Vol. 11, p. 233, 1957.Google Scholar
15. Case, J. Strength of Materials, 3rd Edition. Arnold, London, 1938.Google Scholar