Stability of columns subjected to periodic axial forces of impulsive type
Author:
Norman J. Finizio
Journal:
Quart. Appl. Math. 31 (1974), 455-465
MSC:
Primary 73.35
DOI:
https://doi.org/10.1090/qam/431858
MathSciNet review:
431858
Full-text PDF Free Access
References |
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Additional Information
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
N. J. Finizio, Two classical problems simplified by the introduction of periodic impulsive external forces, Ph.D. dissertation, New York University, 1972
H. Hochstadt, A special Hill’s equation with discontinuous coefficients, NYU Inst. Math. Sci., Div. of EM Res., Report BR-32 (1960)
R. de L. Kronig and W. G. Penny, Quantum mechanics in crystal lattices, Proc. Royal Soc. London, 130, 215–236 (1918)
- S. Lubkin and J. J. Stoker, Stability of columns and strings under periodically varying forces, Quart. Appl. Math. 1 (1943), 215–236. MR 8982, DOI https://doi.org/10.1090/S0033-569X-1943-08982-X
- N. W. McLachlan, Theory and Application of Mathieu Functions, Oxford, at the Clarenden Press, 1947. MR 0021158
- Wilhelm Magnus and Stanley Winkler, Hill’s equation, Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons New York-London-Sydney, 1966. MR 0197830
E. Meissner, Uber Schuettelschwingungen in Systemen mit periodisch veraenderlicher Elastizitaet, Schweizer Bauzeitung, 72, No. 10 (1918)
- Louis A. Pipes, Matrix solution of equations of the Mathieu-Hill type, J. Appl. Phys. 24 (1953), 902–910. MR 56797
- Louis A. Pipes, The dynamic stability of a uniform straight column excited by a pulsating load, J. Franklin Inst. 277 (1964), 534–551. MR 164512, DOI https://doi.org/10.1016/0016-0032%2864%2990373-4
A. Sommerfeld and H. Bethe, Elektronen Theorie der Metalle, in Handbuch der Physik, second ed., Vol. 24II (1933)
- J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932
M. J. O. Strutt, Lamesche Mathieusche und Verwandte Functionen, Ergebnisse der Math. 3, Springer, Berlin (1932)
S. Timoshenko, Vibration problems in engineering, Van Nostrand, Princeton (1928)
A. W. Young, Quasi-periodic solutions of Mathieu’s equation, Proc. Edinburgh Math. Soc. 32 (1914)
E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York (1955)
N. J. Finizio, Two classical problems simplified by the introduction of periodic impulsive external forces, Ph.D. dissertation, New York University, 1972
H. Hochstadt, A special Hill’s equation with discontinuous coefficients, NYU Inst. Math. Sci., Div. of EM Res., Report BR-32 (1960)
R. de L. Kronig and W. G. Penny, Quantum mechanics in crystal lattices, Proc. Royal Soc. London, 130, 215–236 (1918)
S. Lubkin and J. J. Stoker, Stability of columns and strings under periodically varying forces, Quart. Appl. Math. 1, (1943)
N. W. McLachlan, Theory and application of Mathieu functions, Oxford University Press, London (1951)
W. Magnus and S. Winkler, Hill’s equation, Interscience, New York (1966)
E. Meissner, Uber Schuettelschwingungen in Systemen mit periodisch veraenderlicher Elastizitaet, Schweizer Bauzeitung, 72, No. 10 (1918)
L. A. Pipes, Matrix solutions of equations of the Mathieu-Hill type, J. App. Phys. 24 (1953)
L. A. Pipes, The dynamic stability of a uniform straight column excited by a pulsating load, J. Franklin Inst. 277 (1964)
A. Sommerfeld and H. Bethe, Elektronen Theorie der Metalle, in Handbuch der Physik, second ed., Vol. 24II (1933)
J. J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscience, New York (1950)
M. J. O. Strutt, Lamesche Mathieusche und Verwandte Functionen, Ergebnisse der Math. 3, Springer, Berlin (1932)
S. Timoshenko, Vibration problems in engineering, Van Nostrand, Princeton (1928)
A. W. Young, Quasi-periodic solutions of Mathieu’s equation, Proc. Edinburgh Math. Soc. 32 (1914)
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Article copyright:
© Copyright 1974
American Mathematical Society
