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. A remark on Dirichlet boundary condition for the nonlinear equation of motion of a vibrating membrane
   Kikuchi K.
   Nonlinear Analysis, August 2001, vol. 47, no. 2, pp. 1039-1050(12), Ingenta.
4. A Unified Method For Constructing The Dynamic Boundary Stiffness And Boundary Flexibility For Rod, Beam And Circular Membrane Structures
   Chen J.T.; Chung I.L.
   Journal of Sound and Vibration, October 2001, vol. 246, no. 5, pp. 877-899(23), Ingenta.
5. 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.  
6. Application of variational principles to the axial extension of a circular cylindical nonlinearly elastic membrane
   Haddow J.B.; Favre L.; Ogden R.W.
   Journal of Engineering Mathematics, February 2000, vol. 37, no. 1/3, pp. 65-84(20), Ingenta.
7. Comments On “Fundamental Frequency Of A Wavy Non-Homogeneous Circular Membrane”
   Laura P.A.A.; Rossit C.A.; Bambill D.V.
   Journal of Sound and Vibration, December 2000, vol. 238, no. 4, pp. 720-722(3), Ingenta.
8. Wrinkling on stretched circular membrane under in-plane torsion: - bifurcation analyses and experiments
   Miyamura T.
   Engineering Structures, November 2000, vol. 22, no. 11, pp. 1407-1425(19), Ingenta.
9. 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.
10. Strange conserved quantities for the wave equation for elastic membranes.
    Minzoni, A. A.; Vargas, C. A.
    Appl. Math. Lett. 13 (2000), no. 2, 105--109, MathSciNet.  
11. Fundamental Frequency Of A Wavy Non-Homogeneous Circular Membrane
    Wang C.Y.
    Journal of Sound and Vibration, October 1999, vol. 227, no. 3, pp. 682-684(3), Ingenta.
12. 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.
13. Comments On “On The Polygonal Membrane With A Circular Core”
    Laura P.A.A.; Vera S.A.
    Journal of Sound and Vibration, April 1999, vol. 222, no. 2, pp. 331-332(2), Ingenta.
14. The scattering properties of a membrane constrained on a small circular region
    Pang W. M.; Leppington F. G.
    Proceedings: Mathematical, Physical & Engineering Sciences, 1 June 1999, vol. 455, no. 1986, pp. 2067-2089(23), Ingenta.
15. The distribution of eigenfrequencies of anisotropic fractal drums.
    Farkas, Walter; Triebel, Hans
    J. London Math. Soc. (2) 60 (1999), no. 1, 224--236, MathSciNet.  
16. Exact controllability of a coupled vibrating membranes system.
    Ma, Jian Ping
    Saitama Math. J. 16 (1998), 39--51 (1999), MathSciNet.  
17. 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.  
18. Eigenfrequencies of isotropic fractal drums.
    Edmunds, David; Triebel, Hans
    The Maz'ya anniversary collection, Vol. 2 (Rostock, 1998), 81--102, Oper. Theory Adv. Appl., 110, Birkhäuser, Basel, 1999, MathSciNet.  
19. 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.
20. On The Polygonal Membrane With A Circular Core
    Wang C.Y.
    Journal of Sound and Vibration, August 1998, vol. 215, no. 1, pp. 195-199(5), Ingenta.
21. Added Mass Of A Membrane Vibrating At Finite Amplitude
    Minami H.
    Journal of Fluids and Structures, October 1998, vol. 12, no. 7, pp. 919-932(14), Ingenta.
22. Exact controllability of a hybrid system, membrane with strings, on general polygon domains.
    Liu, Bo
    J. Dynam. Control Systems 4 (1998), no. 1, 29--47, MathSciNet.  
23. Stabilization of the position of a circular membrane
    Hashimoto H.; Arai K.; Yoshida S.; Chikuda M.; Obara Y.; Lavrovskii E.K.; Formal'skii A.M.
    Journal of Applied Mathematics and Mechanics, 1997, vol. 61, no. 3, pp. 443-450(8), Ingenta.
24. 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.
25. Non-linear analysis of prestretched circular membrane and a modified iteration technique
    D. C.; S. C.
    International Journal of Solids and Structures, February 1996, vol. 33, no. 4, pp.
    545-553(9), Ingenta.
26. Snowflake harmonics and computer graphics: numerical computation of spectra on fractal drums.
    Lapidus, Michel L.; Neuberger, J. W.; Renka, Robert J.; Griffith, Cheryl A.
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 6 (1996), no. 7, 1185--1210, MathSciNet.  
27. Drums That Sound the Same  
    S. J. Chapman  
    American Mathematical Monthly, Vol. 102, No. 2. (Feb., 1995), pp. 124-138, Jstor.  
28. A finite-difference solution to a two-dimensional vibrating membrane problem using a spreadsheet program
    Kharab A.
    Advances in Engineering Software, 1995, vol. 23, no. 2, pp. 115-120(6), Ingenta.
29. Incremental stresses in loaded orthotropic circular membrane tubes--I. Theory
    Libai A.; Givoli D.
    International Journal of Solids and Structures, July 1995, vol. 32, no. 13, pp.
    1907-1925(19), Ingenta.
30. Some remarks on duality in linear vibration of minimum surface membranes.
    Tong, L.
    Z. Angew. Math. Mech. 75 (1995), no. 4, 318--322, MathSciNet.  
31. 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.
32. Some results concerning the control of strings and membranes.
    Joó, I.
    Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 37 (1994), 267--283, MathSciNet.  
33. Dualities in free vibration of minimum surface membranes.
    Tabarrok, B.; Tong, Liyong
    Trans. ASME J. Appl. Mech. 60 (1993), no. 4, 1020--1026, MathSciNet.  
34. On the pointwise controllability of circular membranes.
    Joó, I.
    Acta Sci. Math. (Szeged) 57 (1993), no. 1-4, 373--399, MathSciNet.  
35. Unilateral problems for vibrating strings or membranes. Current problems of analysis and mathematical physics (Italian)
    Amerio, Luigi
    (Taormina, 1992), 31--46, Univ. Roma "La Sapienza", Rome, 1993, MathSciNet.  
36. 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.  
37. Vibrations of fractal drums, the Riemann hypothesis, waves in fractal media and the Weyl-Berry conjecture.
    Lapidus, M. L.
    Ordinary and partial differential equations, Vol. IV (Dundee, 1992), 126--209, Pitman Res. Notes Math. Ser., 289, Longman Sci. Tech., Harlow, 1993, MathSciNet.  
38. Application of a countable system of nonlinear integral equations to the solvability of a nonlinear equation of the oscillation of a membrane. (Russian)
    Nurekenov, T. K.
    Izv. Akad. Nauk Respub. Kazakhstan Ser. Fiz.-Mat. 1992, no. 5, 30--40, MathSciNet.  
39. Axisymmetric isospectral annular plates and membranes.
    Gottlieb, H. P. W.
    IMA J. Appl. Math. 49 (1992), no. 2, 185--192, MathSciNet.  
40. Beating a Fractal Drum (in Research News)  
    Faye Flam  
    Science, New Series, Vol. 254, No. 5038. (Dec. 13, 1991), p. 1593, Jstor.  
41. 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.  
42. Impulse, work and impact formulas for vibrating membranes subject to single layer forces.
    Amerio, Luigi
    Nonlinear analysis, 61--76, Quaderni, Scuola Norm. Sup., Pisa, 1991, MathSciNet.  
43. Une note sur l'effet d'une cavité d'air sur les vibrations d'une membrane de tambour. (French) [A note on the effect of an air cavity on the vibrations of a drum membrane]
    Capodanno, P.
    Rev. Roumaine Sci. Tech. Sér. Méc. Appl. 35 (1990), no. 3, 263--268, MathSciNet.  
44. On the vibrations of a spherical membrane.
    Komornik, V.
    Houston J. Math. 16 (1990), no. 2, 187--193, MathSciNet.  
45. Notes to some papers of V. Komornik on vibrating membranes.
    Bogmér, A.; Horváth, M.; Joó, I.
    Period. Math. Hungar. 20 (1989), no. 3, 193--205, MathSciNet.  
46. 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.  
47. Perturbation of the eigenvalues of a membrane with a concentrated mass.
    Leal, C.; Sanchez-Hubert, J.
    Quart. Appl. Math. 47 (1989), no. 1, 93--103, MathSciNet.  
48. 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.  
49. Can One Hear the Shape of a Drum? Revisted  
    M. H. Protter  
    SIAM Review, Vol. 29, No. 2. (Jun., 1987), pp. 185-197, Jstor.  
50. 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.  
51. 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.  
52. 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.  
53. Sensitivity of solutions of the linear equation of the vibrations of a membrane to variations in the coefficients of the equation. (Polish)
    Gutowski, Roman
    Mech. Teoret. Stos. 19 (1981), no. 3, 375--384 (1983), MathSciNet.  
54. Bipolar harmonics on a circular drum.
    Nickel, James A.
    Frontiers of applied geometry (Las Cruces, N.M., 1980). Math. Modelling 1 (1980), no. 4, 369--374 (1981), MathSciNet.  
55. Estimate on the fundamental frequency of a drum.
    Taylor, Michael E.
    Duke Math. J. 46 (1979), no. 2, 447--453, MathSciNet.  
56. Harmonic properties of the annular membrane.
    Gottlieb, H. P. W.
    J. Acoust. Soc. Amer. 66 (1979), no. 3, 647--650, MathSciNet.  
57. 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.  
58. The equation of a vibrating general membrane. Minimal submanifolds and geodesics
    Hasegawa, Takuichi
    (Proc. Japan-United States Sem., Tokyo, 1977), pp. 249--254, North-Holland, Amsterdam-New York, 1979, MathSciNet.  
59. 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.  
60. Eigenfrequencies of an Elliptic Membrane  
    B. A. Troesch, H. R. Troesch  
    Mathematics of Computation, Vol. 27, No. 124. (Oct., 1973), pp. 755-765, Jstor.  
61. On two conjectures in the fixed membrane eigenvalue problem.
    Payne, Lawrence E.
    Z. Angew. Math. Phys. 24 (1973), 721--729, MathSciNet.  
62. On hearing the shape of a drum: An extension to higher dimensions.
    Waechter, R. T.
    Proc. Cambridge Philos. Soc. 72 (1972), 439--447, MathSciNet.  
63. Isoperimetric inequality for some eigenvalues of an inhomogeneous, free membrane.
    Bandle, Catherine
    SIAM J. Appl. Math. 22 (1972), 142--147, MathSciNet.  
64. Regolarità di un problema di disequazioni variazionali relativo a due membrane. (Italian)
    Vergara Caffarelli, Giorgio
    Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 50 (1971), 659--662, MathSciNet.  
65. 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.  
66. 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.  
67. Chebyshev polynomial approximations for the L-membrane eigenvalue problem.
    Mason, J. C.
    SIAM J. Appl. Math. 15 1967 172--186, MathSciNet.  
68. 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.  
69. On hearing the shape of a drum.
    Fisher, Michael E.
    J. Combinatorial Theory 1 1966 105--125, MathSciNet.  
70. Sur les fonctions propres des membranes vibrantes couvrant un secteur symétrique de polygone régulier ou de domaine périodique. (French)
    Hersch, Joseph
    Comment. Math. Helv. 41 1966/1967 222--236, MathSciNet.  
71. Some inequalities for the fundamental frequency of a nonhomogeneous membrane.
    Banks, Dallas O.
    J. Soc. Indust. Appl. Math. 13 1965 635--638, MathSciNet.  
72. Une interprétation du principe de Thomson et son analogue pour la fréquence fondamentale d'une membrane. Application. (French)
    Hersch, Joseph
    C. R. Acad. Sci. Paris 248 1959 2060--2062, MathSciNet.  
73. Note to my paper "On membranes and plates".
    Szegö, G.
    Proc. Nat. Acad. Sci. U.S.A. 44 1958 314--316, MathSciNet.  
74. Variation of normal frequencies of membranes and resonators with additional loads. (Russian)
    Dnestrovskii, Yu. N.
    Akust. Z. 4 1958 244--252, MathSciNet.  
75. 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.  
76. On eigenfunctions of the membrane problem.
    Sambasiva Rao, P.
    J. Indian Math. Soc. (N.S.) 17, (1953). 1--20, MathSciNet.  
77. 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.  
78. 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.  
79. Sur la théorie unitaire des valeurs propres des membranes et des plaques encastrées. (French)
    Weinstein, Alexandre
    C. R. Acad. Sci. Paris 210, (1940). 161--163, MathSciNet.  
80. 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