An approximate theory for the dynamic behavior of soap films
Author:
R. W. Dickey
Journal:
Quart. Appl. Math. 40 (1982), 151-157
MSC:
Primary 73K15; Secondary 49F10, 53A10, 58E12
DOI:
https://doi.org/10.1090/qam/666671
MathSciNet review:
666671
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References |
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Additional Information
R. W. Dickey, Dynamic behavior of soap films, Quart. Appl. Math. 24, 97–106 (1966)
A. Foppl, Vorlesungen über technische Mechanik, Bd. 5, G. Teubner, Leipzig 1905
- E. Bromberg and J. J. Stoker, Non-linear theory of curved elastic sheets, Quart. Appl. Math. 3 (1945), 246–265. MR 13355, DOI https://doi.org/10.1090/S0033-569X-1945-13355-7
- Eric Reissner, Rotationally symmetric problems in the theory of thin elastic shells., Proceedings of the Third U.S. National Congress of Applied Mechanics, Brown University, Providence, R.I., June 11-14, American Society of Mechanical Engineers, New York, 1958, pp. 51–69. MR 0101672
- S. Woinowsky-Krieger, The effect of an axial force on the vibration of hinged bars, J. Appl. Mech. 17 (1950), 35–36. MR 0034202
R. Narasimha, Non-linear vibrations of an elastic string, J. Sound Vib. 8, 134–146 (1968)
R. W. Dickey, Dynamic behavior of cylindrical membranes, Int. J. Non-Linear Mech. 6, 729–734 (1971)
G. Bliss, Calculus of variations, Open Court Pub., La Salle Ill., 1925
R. Courant and D. Hilbert, Methods of mathematical physics, V. I. Interscience Publishers, New York, 1962
- R. W. Dickey, The suspension bridge deflection equations, J. Math. Anal. Appl. 24 (1968), 202–211. MR 232565, DOI https://doi.org/10.1016/0022-247X%2868%2990059-0
- R. W. Dickey, Infinite systems of nonlinear oscillation equations related to the string, Proc. Amer. Math. Soc. 23 (1969), 459–468. MR 247189, DOI https://doi.org/10.1090/S0002-9939-1969-0247189-8
- R. W. Dickey, Free vibrations and dynamic buckling of the extensible beam, J. Math. Anal. Appl. 29 (1970), 443–454. MR 253617, DOI https://doi.org/10.1016/0022-247X%2870%2990094-6
R. W. Dickey, Dynamic behavior of soap films, Quart. Appl. Math. 24, 97–106 (1966)
A. Foppl, Vorlesungen über technische Mechanik, Bd. 5, G. Teubner, Leipzig 1905
E. Bromberg and J. J. Stoker, Non-linear theory of curved elastic sheets, Quart. Appl. Math. 3, 246–265 (1945/46)
E. Reissner, Rotationally symmetric problems in the theory of thin elastic shells, 3rd U.S. Nat. Congress of Appl. Mechs., 51–69, 1958
S. Woinowsky-Krieger, The effect of axial force on the vibration of hinged bars, J. Appl. Mechs. 17, 35—36 (1950)
R. Narasimha, Non-linear vibrations of an elastic string, J. Sound Vib. 8, 134–146 (1968)
R. W. Dickey, Dynamic behavior of cylindrical membranes, Int. J. Non-Linear Mech. 6, 729–734 (1971)
G. Bliss, Calculus of variations, Open Court Pub., La Salle Ill., 1925
R. Courant and D. Hilbert, Methods of mathematical physics, V. I. Interscience Publishers, New York, 1962
R. W. Dickey, The suspension bridge deflection equations, J. Math. Anal. Appls. 24, 202–211 (1968)
R. W. Dickey, Infinite systems of nonlinear oscillation equations related to the string, Proc. Amer. Math. Soc. 23, 459–468 (1969)
R. W. Dickey, Free vibrations and dynamic buckling of the extensible beam, J. Math. Anal. Appls. 29, 443–454 (1970)
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Article copyright:
© Copyright 1982
American Mathematical Society