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Original Articles

An Exposition of the Classical Problem of Vibrations of Membranes and Plates

Pages 96-101 | Published online: 21 Aug 2015

References

  • Courant, R. & Hilbert, D., Methods of Mathematical Physics (Interscience Publishers), Vol. I.
  • Polya, G. & Szego, G., Isoperimetric Inequalities in Mathematical Physics (Princeton University Press), 1950.
  • Seth, B. R., “Transverse vibrations of triangular membranes”, Proc. Indian Acad. Sci., ser. A, 12 (1940), 487–90.
  • Seth, B. R., “Transverse vibrations of rectilinear plates”, ibid., ser. A, 25 (1947), 25–29.
  • Lakshmana Rao, S. K., “On the vibrations of triangular membranes”, J. Indian Inst. Sci., 38 (1956), 1–3.
  • Faber, G., “Beweiss dass unter allen homogenen Membranen von gleichen Fluche und gleicher Spannung die kreisformige den tiefsten grundton gibt”, Sitzungs-berichte der Bayrischen Akademie der Wissenshaften, (1923), 169–72.
  • Krahn, E., “Uber eine Rayleigh formulierte Minimaleigenschaft des kreises”, Mathematische Annalen, 94 (1924), 97–100.
  • Kornhauser, E. T. & Stakgold, I., “A variational theorem for Δu+h2u = 0 and its application”, Journal of Mathematics & Physics, 31 (1952), 45–54.
  • Payne, I. E., “Inequalities for eigen values of membranes and plates”, Journal of Rational Mechanics & Analysis, 4 (1955), 517–29.

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