Stability of periodic solutions of the nonlinear string

Author:
R. W. Dickey

Journal:
Quart. Appl. Math. **38** (1980), 253-259

MSC:
Primary 70K20; Secondary 35L10, 73C02

DOI:
https://doi.org/10.1090/qam/580884

MathSciNet review:
580884

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References | Similar Articles | Additional Information

**[1]**G. F. Carrier,*On the nonlinear vibration problem of the elastic string*,Quart. Appl. Math.**3**, 157 (1945) MR**0012351****[2]**R. Narasimha,*Non-linear vibration of an elastic string*, J. Sound Vib.**8**, 134 (1968)**[3]**R. W. Dickey,*Infinite systems of nonlinear oscillation equations related to the string*, Proc. Amer. Math. Soc.**23**, 459 (1969) MR**0247189****[4]**T. Nishida,*A note on the nonlinear vibrations of an elastic string*, Mem. Fac. Eng., Kyoto Univ.,**34**(1971) MR**0279387****[5]**R. W. Dickey,*The initial value problem for a nonlinear semi-infinite string*, Proc. Roy. Soc. Edin.**82A**, 19 (1978) MR**524669****[6]**S. C. Hu,*The initial value problem for a non-linear infinite string*, Ph.D. Thesis, State University of New York at Buffalo, 1979 MR**2630307****[7]**G. S. S. Murthy and B. S. Ramakrishna,*Non-linear character of resonance in stretched strings*, J. Acoust. Soc. Amer.**38**, 461 (1965)**[8]**J. W. Miles,*Stability of forced oscillations of a vibrating string*, J. Acoust. Soc. Amer.**38**, 1855 (1965) MR**0191153****[9]**G. V. Anand,*Non-linear resonance in stretched strings with viscous damping*, J. Acoust. Soc. Amer.**40**, 1517 (1966)**[10]**E. W. Lee,*Non-linear forced vibration of a stretched string*, Br. J. Appl. Phys.**8**, 411 (1957)**[11]**D. W. Oplinger,*Frequency response of a non-linear stretched string*, J. Acoust. Soc. Amer.**32**, 1529 (1960) MR**0120900****[12]**R. W. Dickey,*Infinite systems of nonlinear oscillation equations with linear damping*, SIAM J. Appl. Math.**19**, 208 (1970) MR**0265654****[13]**E. L. Reiss and B. J. Matkowsky,*Nonlinear dynamic buckling of a compressed elastic column*, Quart. Appl. Math.**29**, 245 (1971) MR**0286344****[14]**J. J. Stoker,*Nonlinear vibrations*, Interscience, New York, 1950 MR**0034932****[15]**L. Brillouin,*Wave propagation in periodic structures*, Dover, New York, 1946**[16]**E. A. Coddington and N. Levinson,*Theory of ordinary differential equations*, McGraw-Hill, New York, 1955 MR**0069338**

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Additional Information

DOI:
https://doi.org/10.1090/qam/580884

Article copyright:
© Copyright 1980
American Mathematical Society