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An Integral Transform Solution of the Differential Equation for the Transverse Motion of an Elastic Beam

Published online by Cambridge University Press:  20 January 2009

J. Fulton
J. Fulton
Affiliation:
Department of Technical Mathematics, The University Of Edinburgh
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It is well known* that certain types of partial differential equation may be solved using integral transforms with suitable kernels. In general, these equations may be solved by the classical method of separating variables, but the use of an integral transform yields the solution in a more direct way in the sense that the boundary values are contained in the solution.

It is the purpose of this note to apply this technique to obtain the solution of the differential equation associated with the transverse motion of an elastic beam for a wide class of boundary conditions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 11 , Issue 2 , November 1958 , pp. 87 - 93
Copyright
Copyright © Edinburgh Mathematical Society 1958

References

REFERENCES

(1) Birkhoff, G. D., Trans. Amer. Math. Soc., 9 (1908).Google Scholar
(2) Darboux, G., Leçons sur la Théorie Générale des Surfaces, vol. II (Paris, 1915).Google Scholar
(3) Ince, E. L., Ordinary Differential Equations (London, 1926).Google Scholar
(4) Sneddon, I. N., Fourier Transforms (New York, 1951).Google Scholar
(5) Temple, G., Proc. London Math. Soc., (2), 29, 1929.Google Scholar
(6) Titchmarsh, E. C., Eigenfunction Expansions (Oxford, 1946).Google Scholar
(7) Tranter, C. J., Integral Transforms (London, 1951).Google Scholar