Dynamic Stability of Circular Rods

Previous article Next article Dynamic Stability of Circular RodsStuart Antman and William H. WarnerStuart Antman and William H. Warnerhttps://doi.org/10.1137/0113068PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. J. Stoker, Non-linear vibrations of systems with several degrees of freedom, Proceedings of the Second U. S. National Congress of Applied Mechanics, Ann Arbor, 1954, American Society of Mechanical Engineers, New York, 1955, 33–43 MR0079176 Google Scholar[2] S. Lubkin and , J. J. Stoker, Stability of columns and strings under periodically varying forces, Quart. Appl. Math., 1 (1943), 215–236 MR0008982 0063.03669 CrossrefGoogle Scholar[3] E. Mettler, Eine Theorie der Stabilität der elastischen Bewegung, Ing.-Arch., 16 (1947), 135–146 10.1007/BF00534636 MR0025961 0031.08704 CrossrefGoogle Scholar[4] E. Mettler, Allgemeine Theorie der Stabilität erzwungener Schwingungen elastischer Körper, Ing.-Arch., 17 (1949), 418–449 10.1007/BF00537887 MR0040950 0035.11701 CrossrefGoogle Scholar[5] A. E. H. Love, A treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944xviii+643 MR0010851 0063.03651 Google Scholar[6] John William Rayleigh and , Baron Strutt, The Theory of Sound, Dover Publications, New York, N. Y., 1945Vol. I, xlii+480 pp.; vol. II, xii+504 MR0016009 0061.45904 Google Scholar[7] J. P. Den Hartog, The lowest natural frequency of circular arcs, Philos. Mag., 5 (1928), 400–408 CrossrefGoogle Scholar[8] Karl Federhofer, Dynamik des Bogenträgers und Kreisringes, Springer-Verlag, Vienna, 1950xii+179 MR0040167 CrossrefGoogle Scholar[9] L. V. Kantorovich and , V. I. Krylov, Approximate methods of higher analysis, Translated from the 3rd Russian edition by C. D. Benster, Interscience Publishers, Inc., New York, 1958xv+681 MR0106537 0083.35301 Google Scholar[10] T. E. Lang, Vibrations of thin circular rings. Part II, Tech. Rpt., 32-261, Jet Propulsion Laboratory, 1963 Google Scholar[11] H. R. Bailey and , Lamberto Cesari, Boundedness of solutions of linear differential systems with periodic coefficients, Arch. Rational Mech. Anal., 1 (1958), 246–271 MR0096840 0081.30503 CrossrefISIGoogle Scholar[12] V. V. Bolotin, Dynamic stability of elastic systems, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956, 600–, English transl., Holden-Day, San Francisco, 1964. MR0091033 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Dynamic Stability of Planar Rods of Noncircular Centerline.L. C. Rodgers and W. H. WarnerSIAM Journal on Applied Mathematics, Vol. 24, No. 3 | 17 February 2012AbstractPDF (1351 KB) Volume 13, Issue 4| 1965Journal of the Society for Industrial and Applied Mathematics913-1107 History Submitted:30 September 1964Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113068Article page range:pp. 1007-1018ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics