Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T17:28:44.744Z Has data issue: false hasContentIssue false
  • English
  • Français

Some developments of expansion methods for solving the flutter equations

Published online by Cambridge University Press:  07 June 2016

John Williams
John Williams*
Affiliation:
Aerodynamics Division, National Physical Laboratory
Get access

Summary

In a theoretical flutter analysis, the real zeros x˂0,y˃0, of a stability determinant Δ(√x, y) which is a polynomial in y are required, and can readily be evaluated once the polynomial expansions are known for assigned values of x. When the air loads are estimated on the basis of classical derivative theory, Δ becomes a bivariate polynomial in √x and y of a special type. Direct expansion of the stability determinant becomes too involved when the number of degrees of freedom is large and indirect methods of expansion are needed.

A method of bivariate expansion which uses a framework of lines subject to certain restrictions is examined in Part I, and is applied to a quaternary wing-flutter problem. The analysis shows that frameworks previously proposed, having all intersections outside the flutter quadrant (x˂0, y˃0), demand very high computational accuracy. A new framework is suggested having all intersections inside the flutter quadrant. The improvement in computational accuracy is considerable.

Type
Research Article
Information
Aeronautical Quarterly , Volume 2 , Issue 3 , November 1950 , pp. 209 - 225
Copyright
Copyright © Royal Aeronautical Society. 1950

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Williams, J. (1948). Aircraft Flutter, Part I. R.& M. 2492, Aug. 1948 (A.R.C. Monograph).Google Scholar
2. Frazer, R. A. (1943). A Proposed Method for the Numerical Solution of Flutter and Stability Problems. A.R.C. 7007, Aug. 1943 (Unpublished).Google Scholar
3. Frazer, R. A. (1944). Bi-variate Partial Fractions and their Applications to Flutter and Stability Problems. Proc. Roy. Soc. A, Vol. 185, p. 465, 1946.Google Scholar
4. Frazer, R. A. (1944). Proposed Standard Line Lattice for Flutter Predictions up to Ten Degrees of Freedom, A.R.C. 7770, June 1944 (Unpublished).Google Scholar
5. Price, H. L. (1944). Note on Frazer's Proposed Method for the Numerical Solution of Flutter and Stability Problems. R.& M. 2393, Aug. 1944.Google Scholar
6. Hotelling, H. (1943). Some New Methods in Matrix Calculation. Annals of Mathematical Statistics, Vol. 14, p. 1, 1943.CrossRefGoogle Scholar
7. Wayland, H. (1945). Expansion of Determinantal Equations into Polynomial Form. Quarterly of Applied Mathematics, Vol. 2, p. 277, 1945.CrossRefGoogle Scholar
8. Whittaker, E. T. and Robinson, G. (1937). The Calculus of Observations, 2nd Edn., § 181, Blackie & Son Ltd., 1937.Google Scholar