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Determination of the zeros of a cross-product Bessel function

Published online by Cambridge University Press:  24 October 2008

L. Z. Salchev  and
V. B. Popov
L. Z. Salchev
Affiliation:
Higher Mech. and Electrot. Inst. Sofia, Bulgaria
V. B. Popov
Affiliation:
Higher Mech. and Electrot. Inst. Sofia, Bulgaria
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Extract

In many mechanical and other problems the following equation

is reached, where Jν(α) and Yν(α) are Bessel functions of the first and second kind of any real order ν and β is a positive parameter.

For example, equation (1) is reached in the case of determining the critical load Pcr, for a simply supported strut with a variable inertia moment by a power law, where the power m is any real number.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 477 - 483
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Dinnik, A. N.Prodolnii izgib (Cruchenie, Moskva, 1955).Google Scholar
(2)Timoshenko, S. and Gere, J.Theory of elastic stability (New York, 1961).Google Scholar
(3)Salchev, L. and Mandichev, G.Technicheska misal, III, 101–109 (Bulgaria, 1966).Google Scholar
(4)Papkovich, P.Trudi stroitelnoi mehanica korablja, vol. 4 (Leningrad, 1963).Google Scholar
(5)Janke, E., Emde, F. and Lösch, F.Tafeln höherer funktionen (Stuttgart, 1960).Google Scholar
(6)Kirkham, Don, J. Math. and Phys. 36 (1958), 371–377.CrossRefGoogle Scholar
(7)Watson, G.A treatise on the theory of Bessel functions, 2nd ed. (Cambridge, 1958).Google Scholar
(8)Bessel functions, part III. Zeros and associated values (Cambridge, 1960).Google Scholar
(9)Cochran, , J. Proc. Cambridge Philos. Soc. 62 (1966), 215–226.CrossRefGoogle Scholar
(10)McMahon, , J. Ann. of Math. 9 (1894), 23–30.CrossRefGoogle Scholar
(11)Metcalf, F. and Zlamal, M.Amer. Math. Monthly, 73 (1966), 746–749.CrossRefGoogle Scholar
(12)Willis, D.Proc. Cambridge Philos. Soc. 61 (1965), 425–428.CrossRefGoogle Scholar
(13)Corenev, B.Vvedenie v teorii Beselevih Funczii (Moskva, 1971).Google Scholar
(14)Bessel functions, part II. Functions of positive integer order (Cambridge, 1952).Google Scholar
(15)Tables of Bessel functions of fractional order, vol. I (Columbia Univ. Press, New York, 1948).Google Scholar
(16)Tables of spherical Bessel functions, vol. I and III (Columbia Univ. Press, New York, 1947).Google Scholar