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 | Similar Articles | Additional Information

**[1]**R. W. Dickey,*Dynamic behavior of soap films*, Quart. Appl. Math.**24**, 97-106 (1966)**[2]**A. Foppl,*Vorlesungen über technische Mechanik*, Bd. 5, G. Teubner, Leipzig 1905**[3]**E. Bromberg and J. J. Stoker,*Non-linear theory of curved elastic sheets*, Quart. Appl. Math.**3**, 246-265 (1945/46) MR**0013355****[4]**E. Reissner,*Rotationally symmetric problems in the theory of thin elastic shells*, 3rd U.S. Nat. Congress of Appl. Mechs., 51-69, 1958 MR**0101672****[5]**S. Woinowsky-Krieger,*The effect of axial force on the vibration of hinged bars*, J. Appl. Mechs.**17**, 35--36 (1950) MR**0034202****[6]**R. Narasimha,*Non-linear vibrations of an elastic string*, J. Sound Vib.**8**, 134-146 (1968)**[7]**R. W. Dickey,*Dynamic behavior of cylindrical membranes*, Int. J. Non-Linear Mech.**6**, 729-734 (1971)**[8]**G. Bliss,*Calculus of variations*, Open Court Pub., La Salle Ill., 1925**[9]**R. Courant and D. Hilbert,*Methods of mathematical physics*, V. I. Interscience Publishers, New York, 1962**[10]**R. W. Dickey,*The suspension bridge deflection equations*, J. Math. Anal. Appls.**24**, 202-211 (1968) MR**0232565****[11]**R. W. Dickey,*Infinite systems of nonlinear oscillation equations related to the string*, Proc. Amer. Math. Soc.**23**, 459-468 (1969) MR**0247189****[12]**R. W. Dickey,*Free vibrations and dynamic buckling of the extensible beam*, J. Math. Anal. Appls.**29**, 443-454 (1970) MR**0253617**

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Additional Information

DOI:
https://doi.org/10.1090/qam/666671

Article copyright:
© Copyright 1982
American Mathematical Society