Lower Bounds for Vibration Frequencies of Elastically Supported Membranes and Plates

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Next article Lower Bounds for Vibration Frequencies of Elastically Supported Membranes and PlatesL. E. Payne and H. F. WeinbergerL. E. Payne and H. F. Weinbergerhttps://doi.org/10.1137/0105012PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. Courant and , D. Hilbert, Methoden der Mathematischen Physik I, J. Springer, Berlin, 1931 0001.00501 CrossrefGoogle Scholar[2] G. Faber, Beweis dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt, Bayr. Akad. Wiss. Math.-Nat. Kl. S.-B., (1923), 169–172 Google Scholar[3] E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises, Math. Ann., 94 (1925), 97–100 10.1007/BF01208645 MR1512244 CrossrefGoogle Scholar[4] E. T. Kornhauser and , I. Stakgold, A variational theorem for $\nabla\sp 2u+\lambda u=0$ and its applications, J. Math. Physics, 31 (1952), 45–54 MR0047236 0046.32303 CrossrefISIGoogle Scholar[5] G. Pólya, Remarks on the foregoing paper, J. Math. Physics, 31 (1952), 55–57 MR0047237 0046.32401 CrossrefISIGoogle Scholar[6] G. Szegö, Inequalities for certain eigenvalues of a membrane of given area, J. Rational Mech. Anal., 3 (1954), 343–356 MR0061749 0055.08802 ISIGoogle Scholar[7] H. F. Weinberger, An isoperimetric inequality for the N-dimensional free membrane problem, J. Rational Mech. Anal., 5 (1956), 633–636 MR0079286 0071.09902 ISIGoogle Scholar[8] L. E. Payne, Inequalities for eigenvalues of supported and free plates, Quart. Appl. Math., 16 (1958), 111–120 MR0096440 0084.20705 CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails A Lower Bound for the Eigenvalues of the Elliptic Dirichlet Problem for a General Domain in Terms of Its Characteristic DimensionSIAM Journal on Mathematical Analysis, Vol. 9, No. 4 | 17 February 2012AbstractPDF (480 KB)Isoperimetric Inequalities and Their ApplicationsSIAM Review, Vol. 9, No. 3 | 18 July 2006AbstractPDF (3755 KB)Inequalities for Nonlocal Parabolic and Higher Order Elliptic EquationsSIAM Review, Vol. 9, No. 3 | 18 July 2006AbstractPDF (1199 KB)Stability Inequalities for Semimonotonically Perturbed Nonhomogeneous Boundary ProblemsKarl GustafsonSIAM Journal on Applied Mathematics, Vol. 15, No. 2 | 13 July 2006AbstractPDF (1886 KB)Bounds to Eigenvalues of Rhombical MembranesJames T. StadterSIAM Journal on Applied Mathematics, Vol. 14, No. 2 | 13 July 2006AbstractPDF (1395 KB)Some Inequalities for the Fundamental Frequency of a Nonhomogeneous MembraneDallas O. BanksJournal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 3 | 13 July 2006AbstractPDF (237 KB) Volume 5, Issue 4| 1957Journal of the Society for Industrial and Applied Mathematics171-262 History Submitted:06 May 1957Published online:10 July 2006 InformationCopyright © 1957 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0105012Article page range:pp. 171-182ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics