Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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 | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York (1955) MR 0069338
  • [2] N. J. Finizio, Two classical problems simplified by the introduction of periodic impulsive external forces, Ph.D. dissertation, New York University, 1972
  • [3] H. Hochstadt, A special Hill's equation with discontinuous coefficients, NYU Inst. Math. Sci., Div. of EM Res., Report BR-32 (1960)
  • [4] R. de L. Kronig and W. G. Penny, Quantum mechanics in crystal lattices, Proc. Royal Soc. London, 130, 215-236 (1918)
  • [5] S. Lubkin and J. J. Stoker, Stability of columns and strings under periodically varying forces, Quart. Appl. Math. 1, (1943) MR 0008982
  • [6] N. W. McLachlan, Theory and application of Mathieu functions, Oxford University Press, London (1951) MR 0021158
  • [7] W. Magnus and S. Winkler, Hill's equation, Interscience, New York (1966) MR 0197830
  • [8] E. Meissner, Uber Schuettelschwingungen in Systemen mit periodisch veraenderlicher Elastizitaet, Schweizer Bauzeitung, 72, No. 10 (1918)
  • [9] L. A. Pipes, Matrix solutions of equations of the Mathieu-Hill type, J. App. Phys. 24 (1953) MR 0056797
  • [10] L. A. Pipes, The dynamic stability of a uniform straight column excited by a pulsating load, J. Franklin Inst. 277 (1964) MR 0164512
  • [11] A. Sommerfeld and H. Bethe, Elektronen Theorie der Metalle, in Handbuch der Physik, second ed., Vol. 24II (1933)
  • [12] J. J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscience, New York (1950) MR 0034932
  • [13] M. J. O. Strutt, Lamesche Mathieusche und Verwandte Functionen, Ergebnisse der Math. 3, Springer, Berlin (1932)
  • [14] S. Timoshenko, Vibration problems in engineering, Van Nostrand, Princeton (1928)
  • [15] A. W. Young, Quasi-periodic solutions of Mathieu's equation, Proc. Edinburgh Math. Soc. 32 (1914)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73.35

Retrieve articles in all journals with MSC: 73.35

Additional Information

DOI: https://doi.org/10.1090/qam/431858
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society