Vibrations of twisted beams. II
Authors:
William Boyce and George Handelman
Journal:
Quart. Appl. Math. 16 (1959), 385-395
MSC:
Primary 73.00
DOI:
https://doi.org/10.1090/qam/100997
MathSciNet review:
100997
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Additional Information
- R. C. Di Prima and G. H. Handelman, Vibrations of twisted beams, Quart. Appl. Math. 12 (1954), 241–259. MR 64619, DOI https://doi.org/10.1090/S0033-569X-1954-64619-1
R. Plunkett, Free and forced vibrations of rotating blades, J. Aeronaut. Sci. 18, 278-282 (1951)
F. I. Niordson, Natural frequencies of rotating twisted cantilevered beams, to appear in Proc. IX Intern. Congr. Appl. Mech., Brussels, 1956
E. Kamke, Definite selbstadjungierte Eigenwertaufgaben, I, Math. Z. 45, 759-787 (1939); II, 46, 231-250 (1940); III, 46, 251-286 (1940)
- Jean Kestens, Le problème aux valeurs propres normal et bornes supérieures et inférieures par la méthode des itérations, Acad. Roy. Belg. Cl. Sci. Mém. Coll. in 8$^\circ $ 29 (1956), no. 4, 102 (French). MR 91398
R. V. Southwell, Great Britain—Air Ministry, Aeronaut. Research Communs., Repts. and Memo. 486; H. Lamb and R. V. Southwell, The vibrations of a spinning disc, Proc. Roy. Soc. A99, 272-280 (1921)
- Richard Courant, Über die Anwendung der Variationsrechnung in der Theorie der Eigenschwingungen und über neue Klassen von Funktionalgleichungen, Acta Math. 49 (1926), no. 1-2, 1–68 (German). MR 1555235, DOI https://doi.org/10.1007/BF02543848
William E. Boyce, Effect of hub radius on the vibrations of a uniform bar, J. Appl. Mech. 23, 287-290 (1956)
M. J. Schilhansl, Bending frequency of a rotating cantilever beam, Am. Soc. Mech. Eng., Reprint No. 57-F-6
H. Lo and J. Renbarger, Bending vibrations of a rotating beam, First U. S. Nat. Congr. Appl. Mech., Am. Soc. Mech. Eng., 1952, p. 75
- William E. Boyce, VIBRATIONS OF ROTATING BEAMS, ProQuest LLC, Ann Arbor, MI, 1955. Thesis (Ph.D.)–Carnegie Mellon University. MR 2938649
R. C. DiPrima and G. H. Handelman, Vibrations of twisted beams, Quart. Appl. Math. 12, 241-259 (1954)
R. Plunkett, Free and forced vibrations of rotating blades, J. Aeronaut. Sci. 18, 278-282 (1951)
F. I. Niordson, Natural frequencies of rotating twisted cantilevered beams, to appear in Proc. IX Intern. Congr. Appl. Mech., Brussels, 1956
E. Kamke, Definite selbstadjungierte Eigenwertaufgaben, I, Math. Z. 45, 759-787 (1939); II, 46, 231-250 (1940); III, 46, 251-286 (1940)
Jean Kestens, Le problème aux valeurs propres normal, Mém., Acad. roy. Belg., Classe sci. 29, No. 4 (1956)
R. V. Southwell, Great Britain—Air Ministry, Aeronaut. Research Communs., Repts. and Memo. 486; H. Lamb and R. V. Southwell, The vibrations of a spinning disc, Proc. Roy. Soc. A99, 272-280 (1921)
R. Courant, Über die Anwendung der Variationsrechnung in der Theorie der Eigenschwingungen und über neue Klassen von Funktionalgleichungen, Acta Math. 49, 1-68 (1926)
William E. Boyce, Effect of hub radius on the vibrations of a uniform bar, J. Appl. Mech. 23, 287-290 (1956)
M. J. Schilhansl, Bending frequency of a rotating cantilever beam, Am. Soc. Mech. Eng., Reprint No. 57-F-6
H. Lo and J. Renbarger, Bending vibrations of a rotating beam, First U. S. Nat. Congr. Appl. Mech., Am. Soc. Mech. Eng., 1952, p. 75
William E. Boyce, Vibrations of rotating beams, Ph.D. thesis, Carnegie Institute of Technology, 1955, pp. 68-74
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Article copyright:
© Copyright 1959
American Mathematical Society
