Bibliography for the Vibrating Drum

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  1. An inverse problem for a general vibrating annular membrane in R3 with its physical applications: further results
    Zayed E.M.E.
    Applied Mathematics and Computation, 10 July 2002, vol. 129, no. 2, pp. 203-235(33), Ingenta.
  2. Nailing Down A Vibrating Membrane
    Wang C.Y.
    Journal of Sound and Vibration, November 2001, vol. 247, no. 4, pp. 738-740(3), Ingenta.
  3. On hearing the shape of the three-dimensional multi-connected vibrating membrane with piecewise smooth boundary conditions.
    Zayed, E. M. E.
    Appl. Anal. 79 (2001), no. 1-2, 187--216, MathSciNet.  
  4. Scattering of sound by an infinite membrane fixed on two circular regions
    Leppington F.; Pang W.
    IMA Journal of Applied Mathematics, February 2000, vol. 64, no. 1, pp. 51-72(22), Ingenta.
  5. Fundamental Modes Of A Circular Membrane With Radial Constraints On The Boundary
    Wang C.Y.
    Journal of Sound and Vibration, February 1999, vol. 220, no. 3, pp. 559-563(5), Ingenta.
  6. Can one hear the shape of a smectic drum?
    Ben Amar, Martine; Patrício da Silva, Pedro
    R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454 (1998), no. 1978, 2757--2765, MathSciNet.  
  7. Vibration of circular membrane backed by cylindrical cavity - the Indian musical drum
    Rajalingham C.; Bhat R.B.; Xistris G.D.
    International Journal of Mechanical Sciences, 1 August 1998, vol. 40, no. 8, pp. 723-734(12), Ingenta.
  8. Etransverse Vibrations Of A Square Membrane With An Eccentric Circular Or Quasi-Square Hole
    Gutierrez R.H.; Laura P.A.A.
    Journal of Sound and Vibration, 1997, vol. 201, no. 1, pp. 133-136(4), Ingenta.
  9. Drums That Sound the Same  
    S. J. Chapman  
    American Mathematical Monthly, Vol. 102, No. 2. (Feb., 1995), pp. 124-138, Jstor.  
  10. Evanescence and Bessel functions in the vibrating circular membrane
    Perrin R.; Gottlieb H.P.W.
    European Journal of Physics, 1994, vol. 15, no. 6, pp. 293-299(7), Ingenta.
  11. Dualities in free vibration of minimum surface membranes.
    Tabarrok, B.; Tong, Liyong
    Trans. ASME J. Appl. Mech. 60 (1993), no. 4, 1020--1026, MathSciNet.  
  12. You Can't Hear the Shape of a Drum (in Research News)  
    Barry Cipra  
    Science, New Series, Vol. 255, No. 5052. (Mar. 27, 1992), pp. 1642-1643, Jstor.  
  13. Beating a Fractal Drum (in Research News)  
    Faye Flam  
    Science, New Series, Vol. 254, No. 5038. (Dec. 13, 1991), p. 1593, Jstor.  
  14. How can a drum change shape, while sounding the same? II. Mechanics, analysis and geometry: 200 years after Lagrange, 335--358,
    DeTurck, Dennis; Gluck, Herman; Gordon, Carolyn; Webb, David
    North-Holland Delta Ser., North-Holland, Amsterdam, 1991, MathSciNet.  
  15. Dynamical boundary control of two-dimensional wave equations: vibrating membrane on general domain.
    You, Y. C.; Lee, E. B.
    IEEE Trans. Automat. Control 34 (1989), no. 11, 1181--1185, MathSciNet.  
  16. A Singular Nonlinear Boundary Value Problem: Membrane Response of a Spherical Cap  
    John V. Baxley  
    SIAM Journal on Applied Mathematics, Vol. 48, No. 3. (Jun., 1988), pp. 497-505, Jstor.  
  17. Can One Hear the Shape of a Drum? Revisted  
    M. H. Protter  
    SIAM Review, Vol. 29, No. 2. (Jun., 1987), pp. 185-197, Jstor.  
  18. On the Sound Field Generated by Membrane Surface Waves on a Wedge-Shaped Boundary  
    I. D. Abrahams  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 411, No. 1840. (May 8, 1987), pp. 239-250, Jstor.  
  19. Hearing the shape of an annular drum.
    Gottlieb, H. P. W.
    J. Austral. Math. Soc. Ser. B 24 (1982/83), no. 4, 435--438, MathSciNet.  
  20. The effect of an enclosed air cavity on a rectangular drum.
    Gottlieb, H. P. W.
    J. Austral. Math. Soc. Ser. B 24 (1982/83), no. 3, 343--349, MathSciNet.  
  21. Estimate on the fundamental frequency of a drum.
    Taylor, Michael E.
    Duke Math. J. 46 (1979), no. 2, 447--453, MathSciNet.  
  22. Large Deformation Possible in Every Isotropic Elastic Membrane  
    P. M. Naghdi, P. Y. Tang  
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 287, No. 1341. (Sep. 20, 1977), pp. 145-187, Jstor.  
  23. Problem 73-24, An Inverse Drum Problem (in Problems)  
    L. Flatto, D. J. Newman
    SIAM Review, Vol. 15, No. 4. (Oct., 1973), p. 788, Jstor.  
  24. Eigenfrequencies of an Elliptic Membrane  
    B. A. Troesch, H. R. Troesch  
    Mathematics of Computation, Vol. 27, No. 124. (Oct., 1973), pp. 755-765, Jstor.  
  25. On hearing the shape of a drum: An extension to higher dimensions.
    Waechter, R. T.
    Proc. Cambridge Philos. Soc. 72 (1972), 439--447, MathSciNet.  
  26. One can Hear Whether a Drum has Finite Area  
    Colin Clark, Denton Hewgill  
    Proceedings of the American Mathematical Society, Vol. 18, No. 2. (Apr., 1967), pp. 236-237, Jstor.  
  27. Chebyshev Polynomial Approximations for the L-Membrane Eigenvalue Problem  
    J. C. Mason  
    SIAM Journal on Applied Mathematics, Vol. 15, No. 1. (Jan., 1967), pp. 172-186, Jstor.  
  28. Chebyshev polynomial approximations for the L-membrane eigenvalue problem.
    Mason, J. C.
    SIAM J. Appl. Math. 15 1967 172--186, MathSciNet.  
  29. Can One Hear the Shape of a Drum?  
    Mark Kac  
    American Mathematical Monthly, Vol. 73, No. 4, Part 2: Papers in Analysis. (Apr., 1966), pp. 1-23, Jstor.  
  30. On hearing the shape of a drum.
    Fisher, Michael E.
    J. Combinatorial Theory 1 1966 105--125, MathSciNet.  
  31. A Note on Membrane and Bending Stresses in Spherical Shells  
    Eric Reissner  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 4, No. 4. (Dec., 1956), pp. 230-240, Jstor.  
  32. The Membrane Theory of Shells of Revolution  
    C. Truesdell  
    Transactions of the American Mathematical Society, Vol. 58, No. 1. (Jul., 1945), pp. 96-166, Jstor.  
  33. A Stress Function for the Membrane Theory of Shells of Revolution  
    P. Nemenyi, C. Truesdell  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 29, No. 5. (May 15, 1943), pp. 159-162, Jstor.  
  34. The Tightness of the Teeth, Considered as a Problem Concerning the Equilibrium of a Thin Incompressible Elastic Membrane  
    J. L. Synge  
    Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, Vol. 231. (1933), pp. 435-477, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004