Bibliography of Maurice A. Biot

Books

  1. Mathematical Methods in Engineering, (co-author Th. von Karman), McGraw-Hill Book Company, Inc., 505 pages, New York and London, 1940.
    Foreign translations have been published in the following languages: French, Spanish, Portuguese, Russian, Turkish, Japanese, Polish Hungarian, Italian.
  2. Mechanics of incremental deformations, John Wiley & Sons, Inc., New York, 1965.
    Theory of elasticity and viscoelasticity of initially stressed solids and fluids, including thermodynamic foundations and applications to finite strain.
  3. Variational principles in heat transfer, Oxford University Press 1970.
    A Unified Lagrangian analysis of dissipative phenomena.

Scientific Articles

  1. L'Hydrodynamique moderne et l'aerodynamique, Revue des Eleves des Ecoles Speciales de U.l.Lv., pp. 109-117 et pp. 161-184, 1928, nøs 2-3.
  2. Note sur l'aplatissement des tubes soumis a pression exterieure, Bulletin de la Soc. Belge, Ing. et Ind., pp. 3-7, tome X, nø 4, 1929.
  3. Note sur le calcul d'un arc d'egale resistance, Bulletin de la Soc. Belge, Ing. et Ind., pp. 3-12, tome X, nø 8, 1930.
  4. Sur un procede de guidage des avions, Onde Electrique, 9, nø 107, pp. 520-526, November 1930.
  5. L'Hydrodynamique moderne et ses applications, pp. 235-257, Revue des Questions Scientifiques, September 1930.
  6. Etude theorique sur les courants induits, pp. 94-127, vol. 5, Annales de la Soc. Scientifique de Bruxelles, 1931.
  7. Propriete generale des systemes elastiques soumis a impulsion transitoire, Ann. Soc. Sc. Brux., ser. B, vol. 52, pp. 49-53, 1932.
  8. Sur les extremes de la pression dans un fluide incompressible, Ann. Soc. Sc. Brux., ser. B, vol. 52, pp. 53-54, 1932.
  9. Critical torsional oscillations of a rotating accelerated shaft, Proc. Nat. Ac. Sc., vol. 18, nø 12, pp. 682-89, December 1932.
  10. Theory of elastic systems vibrating under transient impulse with an application to earthquake-proof buildings, Proc. Nat. Ac. Sc., vol. 19, no 2, pp. 262-68.
  11. Quelques acquisitions scicntifiques recenses de l'hydraulique, Bulletin de l'U.I.Lv., 4c Bull., pp. 27-43, 1932.
  12. Contribution a la technique photo-elastique, Ann. Soc. Sc. Brux., vol. 53, ser. B, pp. 13-15, January 1932.
  13. Korrektur fur das quermoment von tragflugeln bei untersuchungen im windkanal mit krcisquerschnitt, Zeitschrift fur Flugtechnik und Motorluftschiffahrt, pp. 1-2, no 15, 1933.
  14. Le probleme de la flexion d'une poutrc sur fondation elastique, Ann. Soc. Sc. de Brux. vol. 53, ser. B, pp. 189-192, October 1933.
  15. Trainee induite d'une aile en diedre, Ann. .Soc; Sc. de Brux., vol. 51, ser. B, pp. 192-194, October 1933
  16. Propriete generale des tensions thermiques en regime stationnaire dans les corps cylindriques. Applications a la mesure photo-elastique de ces tensions, Ann. Soc. Sc. de Brux., vol. 54, ser. B, pp. 14-18, January 1934.
  17. Sur la stabilite de l'equilibre elastique. Equations de l'elasticite d'un milieu soumis a tension initiale, Ann. Soc. Sc. de Brux., vol. 54, ser. B, pp. 18-22, January 1934.
  18. Equations du mouvement d'un fluide renferment des articules en suspension, Ann. Soc; Sc. de Brux., vol. 54, ser. B, pp. 22-24, January 1934.
  19. Etude photo-elastique des tensions de contraction dans un barrage (with H. Smits), Bulletin de U.l.Lv., 4c Bull. Tech., pp. 1-10, 1933.
  20. Theory of vibration of buildings during earthquake, Z.A.M.M., Bd. 14, Heft 4, pp. 213-223, August 1934. 20a. Acoustic spectrum of an elastic body submitted to a shock, Journal of the Acoustical Society of America, vol. V, p. 206-207, January 1934.
  21. A general property of two dimensional thermal-stress distribution, Philosophical Magazine, vol. 19, pp. 540-549, March 1935.
  22. Un cas d'integrabilite de l'equation non lineaire de la chaleur et de la consolidation des sediments argileux, Ann. Soc. Sc. de Brux., Serie B, vol. 55, pp. 106-109, 1935.
  23. Le problcmc dc la consolidtion des matieres argileuses sous une charge, An,'. Soc. Sc. de Brux., ser. B, vol. 55, pp. 110-113, 1935.
  24. (2uadratic wave equation-Flood waves in a channel with quadratic friction, Proc. Nat. Ac. Sc., vol. 21, pp. 436-443, July 1935.
  25. Effect of certain discontinuities on the pressure distribution in a loaded soil, Physics, vol. 6, pp. 367-375, December 1935.
  26. A fourier integral solution of the problem of the bending under a concentrated load of an infinitely long beam resting on an elastic continuum, Proc. Int. Fourth Cong. App. Mech., Cambridge, pp. 161-162, Mass, 1934.
  27. Distributed gravity and temperature loading in two dimensional elasticity replaced by boundary pressures and dislocations, Journal of Applied Mechanics, pp. A 41-45, June 1935.
  28. Effet de certaines discontinuities du soul-sol sur la repartition des pressions dues a une charge, Travaux-Science et Industrie, 5 p., Mai 1936.
  29. Bending of an infinite beam on an elastic foundation, Journal of Applied Mechanics, pp. A 1-7, March 1937.
  30. A hydrodynamic analogy for shearing stress distribution in bending, Journal of Applied Physics, vol. 9, pp. 39-43, January 1938.
  31. Theory of elasticity with large displacements and rotations, Proceedings of the Fifth International Congress of Applied Mechanics, Cambridge USA, pp. 117-122, (ed. Wiley, New York, 1939), 1938.
  32. Theorie de l'elasticite du second ordre avec application a la theorie du flambage, Annales de la Societe Scientifique de Bruxelles, tome LIX, ser. I, pp. 104-112, 1939.
  33. Non linear theory of elasticity and the linearized case for a body under initial stress, Philosophical Magazine, Ser 7, vol XXVII, pp. 468-489, April 1939.
  34. Increase of torsional stiffness of a prisrmatical bar due to axial tension, Journal of Applied Physics, vol. 10, pp. 860-864, December 1939.
  35. Vibration of crankshaft-propeller systems. New method of calculation, Journal of' Aeronautical Sciences, vol. 7, no 3, pp 107-l12, January 1940.
  36. Elastizitats theorie zweiter ordnung mit anwendungen, Zeitschrift fur Ang. Math. u Mech., Bd 20, H 2, pp. 89-99, April 1940.
  37. Coupled oscillations of aircraft engine-propeller systems, Journal of the aeronautical sciences, vol. 7, no 9, pp. 376-382, July 1940.
  38. The influence of initial stress on elastic waves, Journal of Applied Physics, vol. 11, nø 8, pp. 522-530, August 1940.
  39. Equations of finite differences applied to torsional oscillations of crankshafts, Journal of Applied Physics, vol. 11, nø 8, pp. 530-537, August 1940.
  40. General theory of three dimensional consolidation, Journal of Applied Physics, vol. 12, nø 2, pp. 155-164, February 1941
  41. A mechanical analyzer for the prediction of earthquake stresses, Bulletin of the Seismological Society of America, vol 31, nø 2, pp. 151- 171, April 1941.
  42. Consolidation settlement under a rectangular load distribution, (with F.M. Clingan), Journal of Applied Physics, vol. 12, nø 5, pp. 426-430, May 1941.
  43. Consolidation settlement of a soil with an impervious top surface, (with F.M. Clingan), Journal of Applied Physics, vol. 12, nø 7 pp. 578-581, July 1941.
  44. Bending settlement of a slab resting on a consolidating foundation, Journal of Applied Physics, vol. 13, nø 1, pp. 35-40, January 1942.
  45. Analytical and experimental methods in engineering seismology, Proceedings American Society of Civil Engineers, vol. 68, pp. 49-69, January 1942.
  46. Some simplified methods in airfoil theory Journal of the Aeronautical Sciences, vol. 9, nø 5, pp. 185-190, March 1942.
  47. Dynamic loads on airplane structures during landing (with R. L. Bisplinghoff), NACA ARR, nø 4H10, October 1944, pp. 1-55.
  48. The oscillating deformable airfoil of infinite span in compressible flow, Sixth International Congress of Applied Mechanics, Paris, (The proceedings were never published.), September 1946, 5 p.
  49. Low speed flutter and its physical interpretation (with L. Arnold), Jour. Aero. Sciences, 15, pp. 232-236, April 1948.
  50. Loads on a supersonic wing striking a sharp edged gust., Journal of the Aeronautical Sciences, vol. 16, nø 5, pp. 296-300, May 1949.
  51. Transonic drag of an accelerated body, Quarterly of Applied Mathematics, vol. VII, nø 1, pp. 101-105, April 1949.
  52. The interaction of rayleigh and stoneley waves in the ocean bottom, Bulletin of the Seismological Society of America, vol. 42, nø I, pp. 81-93, January 1952.
  53. Propagation of elastic waves in a cylindrical bore containing a fluid, Journal of Applied Physics, vol. 23, nø 9, pp. 997-1005, September 1952.
  54. Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena, Journal of Applied Physics, vol. 25, nø 11, pp. 1385-1391, November 1954.
  55. Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics, vol. 26, nø 2, pp. 182-185, February 1955.
  56. Variational principles in irreversible thermodynamics with application to viscoelasticity, The Physical Review, vol. 97, nø 6, pp. 1463-1469, March 15, 1955.
  57. General solutions of the equations of elasticity and consolidation for a porous material, Journal of Applied Mechanics, Trans. ASME, vol. 78, pp. 91-96, 1956.
  58. Deformation of viscoelastic plates derived from thermodynamics, The Physical Review, vol. 98, nø 6, pp. 1869-1870, June 15, 1955
  59. The divergence of supersonic wings including chordwise bending, Journal of Aeronautical Sciences, vol. 23, nø 3, pp. 237-251, March 1956.
  60. Theory of propagation of elastic waves in a fluid saturated porous solid. I Low frequency range, The Journal of the Acoustical Society of America, vol. 28, nø 2, pp. 168-178, March 1956.
  61. Theory of propagation of elastic waves in a fluid saturated porous solid. II Higher frequency range, The Journal of the Acoustical Society of America, vol. 28, nø 2, pp. 179-191, March 1956.
  62. Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics, vol. 27, nø 3, pp. 240-253, March 1956.
  63. Theory of deformation of a porous viscoelastic anisotropic solid, Journal of Applied Physics, vol. 27, nø 5, pp. 459-467, May 1956.
  64. Applied mathematics an art and a science, Journal of the Aeronautical Sciences, vol. 23, nø 5, pp. 406-410, May 1956.
  65. Dynamics of viscoelastic anisotropic media. Proceedings Fourth Mid-Western Conference on Solid Mechanics, Purdue University (Publication nø 129 engineering experiment station, Purdue university, Lafayette, Indiana), pp. 94-108, September 8-9, 1955.
  66. Variational and lagrangian methods in viscoelasticity. (IUTAM Colloquium Madrid 1955), Deformation and Flow of Solids (Editor R. Grammel) Springer-Verlag, Berlin, pp. 251- 263, 1956.
  67. A New approach to the non linear problems of FM circuits, Quarterly of Applied Mathematics, vol. XV, nø 1, pp. 1-10, April 1957.
  68. The elastic coefficients of the theory of consolidation, Journal of Applied Mechanics, Trans. ASME, vol. 24, pp. 594-601, December 1957.
  69. General theorems on the equivalence of group velocity and energy transport, The Physical Review, vol. 105, nø 4, pp. 1129-1137, February 15, 1957.
  70. Formulation of wave propagation in infinite media by normal co-ordinates with an application to diffraction (with I. Tolstoy), The Journal of the Acoustical Society of America, vol. 29, nø 3, pp. 381-391, March 1957.
  71. The influence of thermal stresses on the aeroelastic stability of supersonic wings, Journal of the Aeronautical Sciences, vol. 24, nø 6, pp. 418-421, June 1957.
  72. Folding instability of a layered viscoelastic medium under compression, Proc. Roy. Soc. A. vol. 242, pp. 444-454, November 1957.
  73. New methods in heat flow analysis with application to flight structures, Journal of Aeronautical Sciences, vol. 24, nø 12, pp. 857-873, December 1957.
  74. Reflection on a rough surface from an acoustic point source, The Journal of the Acoustical Society of America, vol. 29, nø 11, pp. 1193-1200, November 1957.
  75. Some new aspects of the reflection of electromagnetic waves on a rough surface, Journal of Applied Physics, vol. 28, nø 12, pp. 1455-1463, December 1957.
  76. Linear thermodynamics and the mechanics of solids, Proceedings Third U.S. National Congress of Applied Mechanics, Brown University, Providence, R.I. (published by ASME, New York), pp. 1-18, June 1958.
  77. On the reflection of acoustic waves on a rough surface, The Journal of the Acoustical Society of America, vol. 30, nø 5, pp. 479-480, May 1958.
  78. On the reflection of electromagnetic waves on a rough surface, Journal of Applied Physics vol. 29, nø 6, p. 998, June 1958.
  79. The influence of gravity on the folding of a layered viscoelastic medium under compression, Journal of the Franklin Institute, vol. 267, nø 3, pp. 211 -228, March 1959.
  80. Further developments of new methods in heat- flow analysis, Journal of the Aero/Space Sciences, vol. 26, pp. 367-381, June 1959.
  81. Folding of a layered viscoelastic medium derived from an exact stability theory of a continuum under initial stress, Quarterly of Applied Mathematics, vol. XVII, nø 2, pp. 185-204, July 1959.
  82. New thermomechanical reciprocity relations with application to thermal stress analysis, Journal of Aero/Space Sciences, vol. 26, nø 7, pp. 401-408, July 1959.
  83. On the instability and folding deformation of a layered viscoelastic medium in compression, Journal of Applied Mechanics, series E, vol. 26, pp. 393-400, September 1959.
  84. Stability problems of inhomogeneous viscoelastic media. (IUTAM Symposium, Warsaw, September 1958), Non-Homogeneity in Elasticity and Plasticity, Pergamon Press, pp. 311- 321, 1959.
  85. Stability problems of inhomogeneous viscoelastic media, Bulletin de l'Academie Polonaise des Sciences, Serie des Sciences Techniques, vol. VII, nøs 2-3, pp. 165-167, 1959.
  86. Canonical and hamiltonian formalism applied to the sturm-liouville equation (with I. Tolstoy), Quarterly of Applied Mathematics, vol. XVIII, no 2, pp. 163-172, July 1960.
  87. Instability of a continuously inhomogeneous viscoelastic half space under initial stress, Journal of the Franklin Institute, vol. 270, nø 3, pp. 190-201, September 1960.
  88. Thermodynamics and heat-flow analysis by lagrangian methods, Proceedings of the Seventh Anglo-American Aeronautical Conference, pp. 418-431, (published by the institute of aeronautical sciences, New York, N.Y.), 1959.
  89. Trapping of acoustic energy near a source above a submerged elastic plate (with J.H. Rosenbaum), The Journal of the Acoustical Society of America, vol. 33, nø 1, pp. 27-32, January 1961.
  90. Theory of folding of stratified viscoelastic media and its implications in tectonics and orogenesis, The Geological Society of America Bulletin, vol. 72, nø 11, pp. 1595-1620, November 1961.
  91. Experimental verification of the theory of folding of stratified viscoelastic media (with H. Ode and W.L. Roever), The Geological Society of America Bulletin, vol. 72, nø 11, pp. 1621-1632, November 1961.
  92. On the folding of a viscoelastic medium with adhering layer under compressive initial stress (with H. Ode), Quarterly of Applied Mathematics, vol. XIX, nø 4, pp. 351-355, January 1962.
  93. Variational and lagrangian thermodynamics of thermal convection. Fundamental shortcomings of the heat-transfer coefficient, Journal of the Aero/Space Sciences, vol. 29, nø 1, pp. 105-106, January 1962.
  94. Variational analysis of ablation (with H. Daughaday), Jour. of the Aerospace Sciences, vol. 29, nø 2, pp. 228-229, February 1962.
  95. Fundamentals of boundary layer heat transfer with streamwise temperature variations, Jour. of the Aerospace Sciences, vol. 29, nø 5, pp. 558-568, May 1962.
  96. Lagrangian thermodynamics of heat transfer in systems including fluid motion, Jour. of the Aerospace Sciences, vol. 29, nø 5, pp. 568-577, May 1962.
  97. Mechanics of deformation and acoustic propagation in porous media, Jour. of Applied Physics, vol. 33, nø 4, pp. 1482-1498, April 1962.
  98. Theorie generalisee de la propagation acoustique dans un solide poreux dissipatif. Actes du Colloque International C.N.R.S. sur La propagation des ebranlements dans les milieux heterogenes, Marseille, September 1961, pp. 57-65, nø 111, (Published by CNRS Paris, 1962).
  99. Generalized theory of acoustic propagation in porous dissipative media, The Journal of the Acoustical Society of America, vol. 34, nø 5. Part I, pp. 1254-1264, September 1962.
  100. Are we drowning in complexity?, Mechanical Engineering, vol. 85, nø 2, pp. 26-27, 1963.
  101. a) Science and the engineer, Applied Mechanics Reviews, vol. 16, nø 2, pp. 89-90, 1963; b) Science and the engineer, Engineering and Science, vol. XXVI, nø 4, pp. 30-36, 1963 (Caltech Journal); c) Science and the engineer, Scientific World, vol. VII, nø 4, 1963, pp. 9-10. (English, French, Russian, Chinese, German, Spanish).
  102. Internal buckling under initial stress in finite elasticity, Proceedings of the Royal Society, A, vol. 273, pp. 306-328, 1963.
  103. Surface instability in finite anisotropic elasticity under initial stress, Proceedings of the Royal Society, A, vol. 273, pp. 329-339, 1963.
  104. Interfacial instability in finite elasticity under initial stress, Proceedings of the Royal Soeiety, A vol. 273, pp. 340-344, 1963.
  105. Science and the engineer, Journal of Engineering Education, vol. 54, nø 5, pp. 169-170, January 1964.
  106. General fluid-displacement equations for acoustic-gravity waves, The Physics of Fluids, vol. 6, nø 5, pp. 621-626, May 1963.
  107. Variational principles for acoustic-gravity waves, The Physics of Fluids, vol. 6, nø 6, pp. 772-778, June 1963.
  108. Acoustic-gravity waves as a particular case of the theory of elasticity under initial stress, The Physics of Fluids, vol. 6, nø 6, pp. 778-780, June 1963.
  109. Theory of stability and Consolidation of a porous medium under initial stress, Journal of Mathematics and Mechanics, vol. 12, nø 4, pp. 521-542, July 1963.
  110. Theory of stability of multilayered continua in finite anisotropic elasticity, Journal of the Franklin Institute, vol. 276, nø 2, pp. 128-153, August 1963.
  111. Stability of multilayered continua including the effect of gravity and viscoelasticity, Journal of the Franklin Institute, vol. 276, nø 3, pp. 231- 252, September 1963.
  112. Incremental elastic coefficients of an isotropic medium in finite strain, Applied Scientific Research, Section A, vol. 12, pp. 151-167, 1963.
  113. Surface instability of rubber in compression, Applied Scientific Research Section A, vol. 12, pp. 168-182, 1963.
  114. Exact theory of buckling of a thick slab, Applied Scientific Research Section A, vol. 12, pp. 183-198, 1963.
  115. Continuum dynamics of elastic plates and multilayered solids under initial stress, Journal of Mathematics and Mechanics, vol. 12, nø 6, pp. 793-810, November 1963.
  116. Continuum theory of stability of an embedded layer in finite elasticity under initial stress, Quarterly Journal of Mechanics and Applied Mathematics, vol. XVII, Part 1, pp. 17-22, February 1964.
  117. Theory of stability of periodic multilayered continua, Quarterly Journal of Mechanics and Applied Mathematics, vol. XVII, Part 2, pp. 217-224, May 1964.
  118. Theory of buckling of a porous slab and its thermoelastic analogy, Journal of Applied Mechanics (Trans. of the ASME), vol. 31, ser. E, pp. 194-198, June 1964
  119. Theory of internal buckling of a confined multilayered structure, Geological Society of America Bulletin, vol. 75, nø 6, pp. 563-568, June 1964.
  120. Theory of viscous buckling of multilayered fluids undergoing finite strain, The Physics of Fluids, vol. 7, nø 6, pp. 855-861, June 1964.
  121. Validity of thin plate theory in dynamic viscoelasticity (with F.V. Pohle), The Journal of the Acoustical Society of America, vol. 36, nø 6, pp. 1110-1117, June 1964.
  122. Variational analysis of ablation for variable properties (with H.C. Agrawal), Journal of Heat Transfer, (Transactions of the ASME), vol. 86, seer. C, nø 3, pp. 437-442, August 1964.
  123. La ciencia y el ingeniero, Ciencia y Tecnica (Revista del Centro Estudiantes de Ingenieria) Buenos Aires, vol. 133, nø 673, pp. 288-292, 1964.
  124. Internal instability of anisotropic viscous and viscoelastic media under initial stress, Journal of the Franklin Institute, vol. 279, nø 2, pp. 65- 82, February 1965.
  125. Theory of similar folding of the first and second kind, Geological Society of America Bulletin, vol. 76, pp. 251-258, February 1965.
  126. Theory of viscous buckling and gravity instability of multilayers with large deformation, Geo- logical Society of America Bulletin, vol. 76, pp. 371-378, March 1965.
  127. Theory of gravity instability with variable overburden and compaction (with H. Ode), Geophysics, vol. XXX, nø 2, pp. 213-227, April 1965.
  128. Further development of the theory of internal buckling of multilayers, Geological Society of America Bulletin, vol. 76, pp. 833-840, July 1965.
  129. Generalized variational principles for convective heat transfer and irreversible thermodynamics, Journal of Mathematics and Mechanics, vol. 15, nø 2, pp. 177-186, February 1966.
  130. Three-dimensional gravity instability derived from two-dimensional solutions, Geophysics, vol. 31, nø 1, pp. 153-166, February 1966.
  131. Fundamental skin effect in anisotropic solid mechanics, International Journal of Solids and Structures, vol. 2, pp. 645-663, 1966.
  132. Rheological stability with couple stresses and its application to geological folding, Proc. Roy. Soc., ser. A, vol. 298, pp. 402-423, 1967.
  133. Complementary forms of the variational principle for heat conduction and convection, Journal of the Franklin Institute, vol. 283, nø 5. pp. 372-378, May 1967.
  134. Simplified variational and physical analysis of heat transfer in laminar and turbulent flow, The Physics of Fluids, vol. 10, nø 7, pp 1424-1437, 1967.
  135. Edge buckling of a laminated Medium, Inter- national Journal of Solids and Structures, vol. 4, pp. 125-137, 1968.
  136. Generalized boundary condition for multiple scatter in acoustic reflection, Journal of the Acoustical Society of America, vol. 44, nø 6, pp. 1616-1622, 1968.
  137. A new approach to the mechanics of orthotropic multilayered plates, International Journal of Solids and Structures, vol. 8, pp. 475-490, 1972.
  138. Simplified dynamics of multilayered orthotropic viscoelastic plates, International Journal of Solids and Structures, vol. 8, pp. 491-509, 1972.
  139. Theory of finite deformations of porous solids, Indiana University Mathematics Journal, vol. 21, nø 7, pp. 597-620, 1972.
  140. Nonlinear effect of initial stress on crack propagation between similar and dissimilar orthotropic media, Quarterly of Applied Mathematics, vol. XXX, nø 3, pp. 379-406, October 1972.
  141. Lagrangian analysis of multiple scatter in acoustic and electromagnetic reflexion, Bulletin de l'Academie Royale de Belgique (Classe des Sciences), ser. 5, tome LIX, pp. 153-169, 1973.
  142. Nonlinear and semilinear rheology of porous solids, Journal of Geophysical Research, vol. 78, nø 23, pp. 4924-4937, 1973.
  143. Nonlinear thermoelasticity, irreversible thermodynamics and elastic instability, Indiana Univ. Math. Journal, vol. 23, pp. 309-335, 1973.
  144. Buckling and dynamics of multilayered and laminated plates under initial stress, International Journal of Solids and Structures, vol. 10, pp. 419-451, 1974.
  145. Thermoelastic buckling. An unstable thermodynamic equilibrium at maximum entropy, Bulletin de l'Academie Royale de Belgique (Classe des Sciences), ser. 5, tome LX, pp. 116-140, 1974.
  146. Exact simplified nonlinear stress and fracture analysis around cavities in rock, International Journal of Rock Mechanics and Mining Sciences, vol. 11, pp. 261-266, 1974.
  147. A virtual dissipation principle and lagrangian equations in nonlinear irreversible thermodynamics, Bulletin de l'Academie Royale de Belgique (Classe des Sciences), ser. 5, tome LXI, pp. 6-30, 1975.
  148. On a unified thermodynamic approach to a large class of instabilities of dissipative continua, Advances in Chemical Physics, vol. 22, Proc. Conf. on Instabilities & Dissipative structures in hydrodynamics, pp. 13-16. John Wiley & Sons Inc., 1975.
  149. New chemical thermodynamics of open systems. Thermobaric potential, a new concept, Bulletin de l'Academie Royale de Belgique (Classe des Sciences), ser. 5, tome LXII, pp. 239-258, 1976.
  150. Hodograph method of nonlinear stress analysis of thickwalled cylinders and spheres, including porous material, International Journal of Solid and Structures, vol. 12, pp. 613-618, 1976.
  151. Variational-Lagrangian irreversible thermodynamics of nonlinear thermorheology, Quarterly of Applied Mathematics, vol. 34, nø 3, pp. 213- 248, 1976.
  152. Sondage et fracturation hydraulique, U.I.Lv., Bulletin Mensuel, pp. 1-2, 1975.
  153. Variational thermodynamics of viscous compressible heat-conducting fluids, Quarterly of Applied Mathematics, vol. 34, pp. 323-329, 1977.
  154. New chemical thermodynamics of open systems. Thermobaric potential, a new concept, Erratum. Bulletin de l'Academie Royale de Belgique (Classe des Sciences), vol. 62, p. 678, 1976.
  155. Variational-Lagrangian thermodynamics of nonisothermal finite strain mechanics of porous solids and thermomolecular diffusion, International Journal of Solids and Structures, vol. 13, pp. 579-597, 1977.
  156. New fundamental concepts and results in thermodynamics with chemical applications, Chemical Physics, vol. 22, pp. 183-198, 1977.
  157. Variational-Lagrangian irreversible thermodynamics of initially-stressed solids with thermomolecular diffusion and chemical reactions, Journal of the Mechanics and Physics of Solids, vol. 25, pp. 289-307, 1977 and Errata, vol. 26, p. 59, 1978.
  158. Variational-Lagrangian thermodynamics of evolution of collective chemical systems, Chemical Physics, vol. 29, pp. 97-115, 1978.
  159. Notice sur Charles Manneback (avec Marc de Hemptinne), Academie Royale de Belgique, Notices Biographiques, pp. 3-30, Annuaire 1978.
  160. Variational irreversible thermodynamics of heat and mass transfer in porous solids; new concepts and methods, Quart. Appl. Math., vol. 36, pp. 19-38, 1978.
  161. Variational irreversible thermodynamics of physical-chemical solids with finite deformation, Int. J. Solids. Structures. vol. 14, pp. 881-903, 1978.
  162. Nouvelle thermodynamique et mecanique des roches, Sciences de la Terre et Mesures (colloque international J. Goguel, 1977), pp. 329-335, Editions du B.R.G.M., Paris, 1978.
  163. New variational-Lagrangian thermodynamics of viscous fluid mixtures with thermomolecular diffusion, Proc. Roy. Soc., London, A, vol. 365, pp. 467-494, 1979.
  164. New variational irreversible thermodynamics of open physical-chemical continua, Proc. IUTAM Symposium on Variational Methods in the Mechanics of Solids (Evanston Illinois U.S.A., 11-13 Sept. 1978), pp. 29-39. Pergamon Press, New York, 1980.
  165. Dissipation virtuelle et thermodynamique des systemes ouverts, Academie Royale de Belgique. Memoires de la Classe des Sciences. Collection in-8ø-2e eerie, t. XLIV, Fascicule 1, pp. 83-90, 1981.
  166. Charles Manneback., Florilege des Sciences en Belgique. Academie Royale de Belgique (Classe des Sciences), 1980, pp. 371-377.
  167. Generalized Lagrangian thermodynamics of thermorheology, Journal of Thermal Stresses, vol. 4, pp. 293-320, 1981.
  168. Thermodynamic principle of virtual dissipation and the dynamics of physical-chemical fluid mixtures including radiation pressure, Quarterly of Applied Mathematics, vol. 39, pp. 517-540, 1982.
  169. Generalized Lagrangian equations of nonlinear reaction-diffusion, Chemical Physics, vol. 66, pp. 11-26, 1982.
  170. Fundamentals of generalized rigidity matrices for multilayered media, Bulletin of the Seismological Society of America, vol. 73, pp. 749-763, 1983.
  171. Fracture penetration through an interface (with W.L. Medlin and L. Masse), Society of Petroleum Engineers Journal, pp. 857-869, December 1983.
  172. Mecanique et plissements tectoniques, Bulletin de la Societe belge de Geologie, vol. 93, pp. 147-150, 1984.
  173. New variational-Lagrangian irreversible thermodynamics with application to viscous flow, reaction-diffusion and solid mechanics, Advances in Applied Mechanics, vol. 24, pp. 1-91. Academic Press Inc., Orlando, Florida, 1984.
  174. New stability criteria for reaction-diffusion, Chemical Physics, vol. 92, pp. 227-234, 1985.
  175. Variational-Lagrangian analysis of aquifers with application to artesian wells (with A. Delmer), Water Resources Research, vol. 21, nø 2, pp. 249-255, 1985.
  176. Simplified stability criteria for nonconservative dynamical systems with application to wing flutter, Academie Royale de Belgique. Bull. de la Classe des Sciences, 5e serie, T. LXXI, 1985 1-2, pp. 53-62.
  177. A two-dimensional theory of fracture propagation (with L. Masse and W.L. Medlin), S.P.E. (Society of Petroleum Engineers) Production Engineering, January 1986, pp. 17-30.
  178. Temperature analysis in hydraulic fracturing (with L. Masse and W.L. Medlin), S.P.E. Journal of Petroleum Technology, Nov. 1987. pp. 1389-1397.

Scientific Reports

Aeronautical Laboratory California Inst. Tech.

Nø 1. Vibration analysis of a wing carrying large concentrated weights. M.A. Biot, August 1941.

Nø la. Flutter analysis of a wing carrying large concentrated weights. M.A. Biot, January 1942.

Nø 3. Electric network model of flexure torsion flutter. M.A. Biot and T.H. Wiancko, September 1941.

Nø 4. Flutter analysis of the B-24 C Twin Tail. M.A. Biot, August 1942.

Nø 5. Aerodynamic theory of the oscillating wing of finite Span. M.A. Biot and C.T. Boehnlein, September 1942.

Nø 6. Three dimensional aerodynamic theory applied to flutter analysis. M.A. Biot, December 1942.

Nø 8. Theory of electrical flutter predictor for three degrees of freedom. M.A. Biot and T.H. Wiancko, January 1943.

Cornell Aeronautical Laboratory

Report 1. Chordwise divergence The two-dimensional case. CAL/CM-427, December 1947.

Report 2. An approximate treatment of some simple three-dimensional cases. CAL/CM-470, May 1948.

Report 3. General method for the two-dimensional case. CAL/CM-506, September 1948.

Report 4. Some exact solutions based on plate theory. CAL/CM 580, November 1949.

Report 5. Stability of cantilever solid wings of symmetric cross-section and without sweep. CAL/CM 622, May 1950.

Report 6. Solution of the divergence problem by the use of generalized co-ordinates. CAL/CM 730, March 1952.

New expressions for the output of an FM Receiver with application to problems of interference (with S. Kaufman) CAL Rep. BE-745-T-134, August 1956.

OSRD

Dynamic stability of bombs and projectiles. NDRC Div. A. Sect. C, OSRD Contract OEMsr - 418 California Institute of Technology
Chapter I. Forces on a solid moving through an ideal fluid. July 1942.
Chapter II. Stability derivatives in a real fluid. July 1942.
Chapter III. Stability of the rectilinear trajectory in air and water neglecting gravity. September 1942.
Chapter IV. Stability of the vertical fall. May 1943.

The mechanism of water entry of projectiles. NDRC Div. A Sect. C, OSRD Contract OEMsr - 418 California Institute of Technology, September 1943.

USAF

Aerodynamics of the oscillating airfoil in compressible flow (with S.N. Karp, S.S. Shu, H. Weil).
I. Theory USAF Tech. Rep. F-TR-1167-ND
II. Graphical and numerical data. USAF Tech. Rep. F-TR-1195-NC (CDAM A-9-M Brown university).

Investigation of aileron compressibility flutter (with Lee Arnold) USAF-AMC Wright Patterson AF Base AF Tech. Rep. Nø 6341, August 1950. (declassified)

Biot et Arnold

Theory of armor penetration. Contract DA-30-069- ORD-33, ballistic research laboratories, ordnance cors, department of the army.
Report nø 1 February 1951.
Report nø 2 January 1952.
Report nø 3 January 1953.

Cours abrege pour professeurs de mathematique et de science, University College, Londres

The function of mathematics in our civilization. April 1958, printed by Shell Development Company.

Liste des brevets deposes par M.A. Biot en Belgique, en France et aux Etats-Unis

  1. Linkage mechanism for steering of vehicles, Belgian patent 368, 623, March 15, 1930.
    A linkage system which provides an exact kinematic solution to the problem of differential turning of the wheels for steering of automobiles and other vehicles.
  2. Radio guidance system for ships and aircraft, Belgian patent 372, 520, August 11, 1930.
    (Dispositif emetteur recepteur realisant le reperage radioelectrique integral sans ondes dirigees.) The principle was described by M.A. Biot in a paper << Sur un procede de guidage des avions >> published in l'Onde Electrique, vol. 9, nø 107, pp. 520-526, November 1930. Low frequency radio waves are transmitted from a main transmitter and its slave stations on synchronized frequencies. The transmitters are located about a hundred miles apart and the radio waves form a precise grid pattern of interference and phase difference. It provides an all-weather flight position picture for aircraft, sea-going ships, etc. The principle has received wide application and has been incorporated in the Bendix-Decca system now used throughout the world. Other trade names for these systems are Dectra, Delrac and Navarho.
  3. Electrical synchronization of gun firing, through aircraft propeller disc, Belgian patent 37B, 042, March 16, 1931. Achievement of precise synchronization in the firing of guns and machine guns through aircraft propeller disc by substituting an electrical firing system for the mechanical one.
  4. Aircraft turbo-compound engine, French patent 808, 770, November 4, 1935. An aircraft engine combining a piston engine and a two-stage gas turbine. The patent claims are based on a detailed design carried out over a number of years in collaboration with L. Lvoff, director of << La Precision >> in Brussels and now chief engineer of the Machine Tool Division of << La Brugeoise >>, Belgium. Specific weight and fuel consumption were predicted and fully confirmed by recent development. The principle was incorporated in the Wright Aeronautical compound engine. The invention was disclosed to technical and executive personnel of Wright Aeronautical and discussed at their Patterson, New Jersey, plant in June 1936.
  5. Flutter predicting apparatus, Maurice A. Biot and Thomas H. Wiancko U.S. Patent Office 2448698, September 7, 1948.
    Application, October 21, 1944. Electronic analog computer for the prediction of airplane flutter. An important novel feature was the design of a circuit which incorporates the effect of vorticity shedding of an oscillating wing.
  6. Hydraulic fracturing method to control vertical fracture height, J.L. Fitch, L. Masse, W.L. Medlin, M.A. Biot U.S. patent office 3851709, December 3, 1974.
    Method of controlling height of fracture so that it does not extend vertically into adjacent formations on top and bottom.
  7. Harmonic oscillator for measuring dynamic elastic constants of rock materials. Maurice A. Biot, William L. MEDEIN, Lucien MASSE, U.S. patent office 4 412 452, November 1, 1983.
    A simple harmonic oscillator for use in measuring dynamic elastic constants of rock material samples includes a pair of masses vertically suspended by a pair of wires with the rock sample between them acting as a spring.

Source: Acedemie Royale de Belgique, Annuaire 1990, Extrait, Notice sur Maurice Anthony Biot, par A. Delmer et A. Jaumotte, Bruxelles-Palais des Academies.

 

 

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