BIBLIOGRAPHY

Abramowitz, M. and Stegun, I.A. (1970) Handbook of Mathematical Functions. Dover, New York, U.S.A.

Anderson, D.L (1958a) Preliminary results and review of sea ice elasticity and related studies. Transactions of the Engineering Institute of Canada 2, 116-122.

Anderson, D.L. (1958b) A model for determining sea ice properties. In Arctic Sea Ice, Publication 598, National Academy of Sciences - National Research Council, Wash­ington D.C., U.S.A., 148-152.

Anderson, D.L. (1960) The physical constants of sea ice. Research 13, 310-318. Anderson, D.L. and Weeks, W.F. (1958) A theoretical analysis of sea ice strength. Trans­

actions of the American Geophysical Union 39, 632-640. Arakawa, K (1955) Growth of ice crystals in water. Journal of Glaciology 17, 463-464. Ashby, M.F. and Duval, P. (1985) The creep of polycrystalline ice. Cold Regions Science

and Technology 11, 285-300. Ashton, G.D. (1986) River and Lake Engineering. ed. G.D. Ashton, Water Resources

Publications, Colorado, U.S.A. Assur, A. (1956) Airfields on floating ice sheets. U.S. Army SIPRE Report 36, Cold

Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A. Assur, A. (1958) Composition of sea ice and its tensile strength. In Arctic Sea Ice, Publi­

cation 598, National Academy of Sciences - National Research Council, Washington D.C., U.S.A., 106-138.

Assur, A. (1961) Traffic over frozen or crusted surfaces. Proceedings of the First Interna­tional Conference on Mechanics of Soil- Vehicle Systems, Edizioni Minerva Technica, Torino, Italy, 913-923.

Assur, A. and Weeks, W.F. (1964) Growth, structure and strength of sea ice. U.S. CRREL Research Report 135, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A.

Bates, H.F. and Shapiro, L.H. (1980) Breaking ice with gravity waves. Journal of Energy Resources Technology 102, 148-153.

Bates, H.F. and Shapiro, L.H. (1981) Stress amplification under a moving load on floating ice. Journal of Geophysical Research 86, 6638-6642.

Beltaos, S. (1981) Field studies on the response of floating ice sheets to moving loads. Canadian Journal of Civil Engineering 8, 1-8.

Bennington, KO. (1963) Some crystal growth features of sea ice. Journal of Glaciology 4,669-689.

Bennington, KO. (1967) Desalination features in natural sea ice. Journal of Glaciology 6,845-857.

Biderman, V.L. (1952), Vibrations caused by moving loads (In Russian). In Osnovy Sovre­mennykh Metodov Rascheta na Prochnost v Mashinostoenii, by S. D. Ponomarev, V.L. Biderman et al., Mashgiz, Moscow, 198-202.

Bogacz, R. (1968) Interaction between a moving set of nonlinear oscillators and a traveling wave. Proceedings of Vibration Problems 1, 55-77.

Booth, J.D. (1962) Railways of Southern Quebec. Railfare Enterprises Ltd., Toronto, Canada.

Bukatov, A.E. (1981) Influence of a longitudinally compressed elastic plate on the non­stationary wave motion of a homogeneous liquid. Fluid Dynamics 15, 687-693.

Bukatov, A.E. and Cherkesov, L.V. (1973) Transient vibrations of an elastic plate floating on a liquid surface. Soviet Journal of Applied Mechanics 6, 878-883.

213

214 BIBLIOGRAPHY

Bukatov, A.E. and Yaroshenko, A.A. (1986) Evolution of three-dimensional gravitation­ally warped waves during the movement of a pressure zone of variable intensity. Journal of Applied Mechanics and Technical Physics 27, 676-682.

Bukatov, A.E. and Zharkov, V.V. (1989) Three-dimensional bending gravitational oscil­lations near moving pressure regions. Journal of Applied Mechanics and Technical Physics 30, 490-497.

Cammaert, A.B. and Muggeridge, D.B. (1988) Ice Interaction with Offshore Structures. Van Nostrand Reinhold, New York, U.S.A.

Cherepanov, N.V. (1971) Spatial arrangement of sea ice crystal structure. Problemy Ark­tiki i Antarktiki 38,176-181.

Choi, K. and Karr, D.G. (1989) A damage model for uniaxial creep and cyclic loading of polycrystalline ice. Proceedings of the Eighth International Offshore Mechanics and A rctic Engineering Symposium 4 American Society of Mechanical Engineers, Den Hague, Holland, 75-82.

Cole, D.M. (1990) Cyclic loading of saline ice: initial experimental results. Proceedings of the Ninth International Offshore Mechanics and Arctic Engineering Symposium 4, American Society of Mechanical Engineers, Houston, U.S.A., 265-271.

Cole, D.M. (1991) Anelastic straining in polycrystalline ice. Proceedings of the Sixth Inter­national Speciality Conference on Cold Regions Engineering, ed. D. Sodhi, Lebanon, New Hampshire, U.S.A., 504-518.

Cole, D.M. (1992) Ice physics and micromechanics: a review of selected topics. Proceedings of the Eleventh International Association for Hydraulic Research Ice Symposium 2, Banff, Alberta, Canada, 1087-1099.

Cole, D.M. (1993) The effect of creep on the constitutive behavior of saline ice at low strains. Applied Mechanics Division 163: Ice Mechanics, American Society of Me­chanical Engineers, 261-271.

Cole, D.M. (1994) The effect of temperature and microstructure on the constitutive behaviour of ice at low strains. Proceedings of the Twelth International Association for Hydraulic Research Ice Symposium 3, Trondheim, Norway. 1051-1058.

Cole, D.M. (1995) A model for the anelastic straining of saline ice subjected to cyclic loading. Philosophical Magazine A. 72 231-248.

Cole, D.M. and Durell, G.D. (1995a) The effect of c-axis alignment on the constitutive behaviour of sea ice at low strains. Applied Mechanics Division 207: Ice Mechanics American Society of Mechanical Engineers, Los Angeles, U.S.A., 189-199.

Cole, D.M. and Durell, G.D. (1995b) The cyclic loading of saline ice. Philosophical Mag­azine A. 72 209-230.

Coleman, B.D. and Noll, W. (1961) Foundations of linear viscoelasticity. Reviews of Modern Physics 33, 239-249.

Cox, G.F.N. and Weeks, W.F. (1974) Salinity variations in sea ice. Journal of Glaciology 13, 109-120.

Cox, G.F.N. and Weeks, W.F. (1975) Brine drainage and initial salt entrapment in NaCI ice. CRREL Research Report 345, Cold Regions Research and Engineering Labora­tory, Hanover, New Hampshire, U.S.A.

Cox, G.F.N. and Weeks, W.F. (1983) Equations for determining the gas and brine vol­umes in sea ice samples. Journal of Glaciology 29, 306-316.

Cox, G.F.N. and Weeks, W.F. (1988) Profile properties of first-year sea ice CRREL Re­search Report 88-13, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A.

Crandall, S.H. (1957) The Timoshenko beam on an elastic foundation. Proceedings of the Third Midwestern Conference on Solid Mechanics, Ann Arbor, Michigan, U.S.A., 146-159.

Dally, J.W. and Riley, W.F. (1965) Experimental Stress Analysis. McGraw-Hill, New York, U.S.A. 422-445.

Davys, J.W. (1984) Waves in floating ice plates. M.Sc. thesis, University of Waikato, New Zealand.

BIBLIOGRAPHY 215

Davys, J.W., Hosking, R.J. and Sneyd, A.D. (1985) Waves due to a steadily-moving source on a floating ice plate. Journal of Fluid Mechanics 158, 269-287.

Doronin, Yu.P. and Kheysin, D.Ye. (1975) Sea Ice. Amerind Publishing Co., Pvt. Ltd., New Delhi, India.

Dorr, J. (1943) Der unendliche, federnd gebettete Balken unter dem Einfluss einer gleich­massig bewegten Last. Ingenieur-Archiv 14, 167-192.

Dorr, J. (1948) Das Schwingungsverhalten eines federnd gebetteten, unendlich langen Balkens. Ingenieur-Archiv 16, 287-298.

Duffy, D.G. (1991) The response of floating ice to a moving, vibrating load. Cold Regions Science and Technology 20, 51-64.

Eide, L.I. and Martin, S. (1975) The formation of brine drainage features in young sea ice. Journal of Glaciology 14, 137-154.

Eyre, D. (1977) The flexural motion of a floating ice sheet induced by moving vehicles. Journal of Glaciology 19, 555-570.

Findley, W.N., Lai, J.S. and Onaran, K. (1976) Creep and Relaxation of Nonlinear Vis­coelastic Materials. North-Holland Series in Applied Mathematics and Mechanics, vol. 18, ed. H.A. Lauwerier and W.T. Koiter, Amsterdam, The Netherlands.

Fletcher, N.H. (1970) The Chemical Physics of Ice. Cambridge University Press, Cam­bridge, England.

Fliigge, W. (1975) Viscoelasticity. Springer, New York, U.S.A. Frankenstein, G. and Garner, R. (1967) Equations for determining the brine volume of

sea ice from -0.5° C to -22.9° C. Journal of Glaciology 6, 943-944. Frost, H.J. and Ashby, M.F. (1982) Deformation-mechanism maps: the plasticity and

creep of metals and ceramics. Pergamon Press, Oxford, England .. Fryba, L. (1960) Schwingungen des unendlichen, federnd gebetteten Balkens unter

der Wirkung eines unrunden Rades. Zeitschrijt fur Angewandte Mathematik und Mechanik 40, 170-184.

Fryba, L. (1972) Vibration of Solids and Structures Under Moving Loads. Noordhoff International Publishing, Groningen, The Netherlands.

Fung, Y.C. (1965) Foundations of Solid Mechanics. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, U.S.A.

Glen, J.W. (1955) The creep of polycrystalline ice. Proceedings of the Royal Society of London, A 228, 519-538.

Glen, J.W. (1987) Fifty years of progress in ice physics. Journal of Glaciology, Special Issue, 52-59.

Gold, L.W. (1971) Use of ice covers for transportation. Canadian Geotechnical Journal 8, 170-18!.

Gold, L.W. (1994) The elastic modulus of columnar-grain fresh-water ice. Annals of Glaciology 19, 13-18.

Goloskokov, E.G. and Filippov, A.P. (1962) Steady vibrations of a beam on an elas­tic foundation subjected to a moving load of constant velocity (in Russian). Trudy Laboratorii Gidravlicheskikh Mashin 10, Akademiya Nauk S.S.S.R., Izdatel'stvo Akademiya Nauk Ukrain. S.S.R., Kiev.

Goodman, D.J. and Holdsworth, R. (1978) Continuous surface strain measurements on sea ice and on Erebus Glacier Tongue, McMurdo Sound, Antarctica. Antarctic Jour­nal of the United States 13, 67-70.

Goure, L. (1962) The Siege of Leningrad. Stanford University Press, California, U.S.A. Gow, A.J. and Langston, D. (1977) Growth history of lake ice in relation to its strati­

graphic, crystalline and mechanical structure. CRREL Research Report 77-1, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A.

Graffi, D. (1982) Mathematical models and waves in linear viscoelasticity. In Wave Prop­agation in Viscoelastic Media, ed. F. Mainardi, Pitman, Boston, U.S.A., 1-27.

Greenhill, A.G. (1887) Wave motion in hydrodynamics. American Journal of Mathemat­ics 9, 62-112.

Harris, J. (1977) Rheology and Non-Newtonian Flow. Longman, London, England.

216 BIBLIOGRAPHY

Hegemier, G.A. (1968) On nonlinear steady-state solution to moving load problems. Quarterly of Applied Mathematics 26, 239-248.

Hertz, H. (1884) Uber das Gleichgewicht schwimmender elastischer Platten. Annalen der Physik und Chemie 22 449-455. (English translation: On the equilibrium of float­ing elastic plates. In Miscellaneous Papers by H. Hertz, 1896, Macmillan, London, England, 266-272.

Hillig, W.B. (1958) The kinetics of freezing of ice in the direction perpendicular to the basal plane. In Growth and Perfection of Crystals, Proceedings of a Conference on Crystal Growth, John Wiley & Sons, New York, U.S.A., 350-360.

Hinchey, M.J. (1986) Floating ice roads and runways: critical speed phenomena. Canadian Aeronautics and Space Journal 32, 139-147.

Hinchey, M.J. (1987) Transport over floating ice sheets. Proceedings of the Sixth Interna­tional Offshore Mechanics and Arctic Engineering Symposium 4, American Society of Mechanical Engineers, Houston, U.S.A., 321-328.

Hobbs, P.V. (1974) Ice Physics. Clarendon Press, Oxford, U.K. Holl, D.L. (1950) Dynamic loads on thin plates on elastic foundations. Applied Mathe­

matics Symposium of the American Mathematical Society 3,107-116. Hosking, R.J., Sneyd, A.D. and Waugh, D.W. (1988) Viscoelastic response of a floating

ice plate to a moving load. Journal of Fluid Mechanics 196,409-430. Hovey, B.K. (1933) Beitrag zur Dynamik des geraden Eisenbahngleises. Dissertation,

University of Gottingen, Germany. Hunter, S.C. (1976) Mechanics of Continuous Media. Ellis Horwood Ltd., Chichester,

England. Hutter, K. (1975a) A general non-linear viscoelastic plate theory and its applications to

floating ice. Acta Mechanica 21, 313-327. Hutter, K. (1975b) Floating sea ice plates and the significance of the dependence of the

Poisson ratio on brine volume. Proceedings of the Royal Society of London, A 343, 85-108.

Hutter, K. (1978) On the mechanics of floating ice sheets. Mitteilungen der Versuch­sanstalt fUr Wasserbau, Hydrologie und Glaziologie 28, ETH Ziirich, Switzerland.

Ivanov, K.E., Kobeko, P.P. and Shulman, A.R. (1946) Deformation of an ice cover under moving loads (in Russian). Zhurnal Tekhnicheskoi Fiziki XVI, 257-262.

Kennett, B.L.N. (1983) Seismic Wave Propagation in Stratified Media. Cambridge Uni­versity Press, Cambridge, England.

Kenney, J.T. (1954) Steady-state vibrations of beam on elastic foundation for moving loads. Journal of Applied Mechanics 21, 359-364.

Kerr, A.D. (1972) The continuously supported rail subjected to an axial force and moving load. International Journal of Mechanical Sciences 14, 71-78.

Kerr, A.D. (1976) The bearing capacity of floating ice places subjected to static or quasi­static loads. Journal of Glaciology 17, 229-268.

Kerr, A.D. (1981) Continuously supported beams and plates subjected to moving loads - a survey. Solid Mechanics Archives 6, 401-449.

Kerr, A.D. (1983) The critical velocities of a load moving on a floating ice plate that is subjected to in-plane forces. Cold Regions Science and Technology 6, 267-274.

Kerr, A.D. and Haynes, F.D. (1988) On the determination of the average Young's mod­ulus for a floating ice cover. Cold Regions Science and Technology 15, 39-43.

Kerr, A.D. and Kwak, S.S. (1993a) The semi-infinite plate on a Winkler base, free along the edge, and subjected to a vertical force. Archives of Applied Mechanics 63, 210-218.

Kerr, A.D. and Kwak, S.S. (1993b) The clamped semi-infinite plate on a Winkler base subjected to a vertical force. Quarterly Journal of Mechanics and Applied Mathemat­ics 46, 457-470.

Kerr, A.D. and Palmer, W.T. (1972) The deformations and stresses of floating ice plates. Acta Mechanica 15, 57-72.

Ketcham, W.M. and Hobbs, P.V. (1967) The preferred orientation in the growth of ice

BIBLIOG RAPHY 217

from the melt. Journal of Crystal Growth 1, 263-270. Ketcham, W.M. and Hobbs, P.V. (1969) Direct measurements of the ice-water interfacial

temperature for two crystallographic orientations during the freezing of pure water. Journal of Crystal Growth 6, 113-115.

Kheysin, D. Yeo (1963) Moving load on an elastic plate which floats on the surface of an ideal fluid (in Russian). Izvestiya Akademii Nauk S.S.S.R., Otd. Tekh. Nauk, Mekhanika i Mashinostroenie 1, 178-180.

Kheysin, D. Yeo (1964) On the problem of the elastic-plastic bending of an ice cover (in Russian). Trudy Arkticheskii i Antarkticheskii Nauchno-Issledovatel'skii Institut 267, 143-149.

Kheysin, D. Yeo (1967) Dynamics of Floating Ice Covers (in Russian). Gidrometeoro­logicheskoe Izdatel'stvo, Leningrad, 1967. Technical Translation FSTC-HT-23-485-69, U.S. Army Foreign Science and Technology Center.

Kheysin, D. Yeo (1973) Some unsteady-state problems in ice-cover dynamics. In Studies in Ice Physics and Ice Engineering, ed. G.N. Yakovlev, Israel Program for Scientific Translations, 69-78.

Kingery, W.D. and Goodnow, W.H. (1963) Brine migration in salt ice. In Ice and Snow, Properties, Processes and Applications, ed. W.D. Kingery, M.LT. Press, Cambridge, Massachusetts, U.S.A., 237-247.

Knight, C.A. (1962) Studies of Arctic lake ice. Journal of Glaciology 4, 319-336. Kogan, A. Ya. (1968) Vibration of a rail when subjected to a moving and varying load (in

Russian). Vestnik, Vsesoyznyi Nauchno-Issledovatel'skii, Institut Zh/D Transporta, 27,7-1l.

Krakauer, J. (1987) Truckers brave the barren lands to supply an Arctic gold mine. Smithsonian 18-8, 129-139.

Kubo, Y. (1980) Introductory Remarks on Iceological Engineering (in Japanese). Hyokogakukankokai, Tokyo, Japan.

Lake, R.A. and Lewis, E.L. (1970) Salt rejection by sea ice during growth. Journal of Geophysical Research 75, 583-597.

Lamb, H. (1962) Hydrodynamics. 6th Edition (reprinted), Cambridge University Press, Cambridge, England.

Langhorne, P.J. (1983) Laboratory experiments on crystal orientation in NaCI ice. Annals of Glaciology 4, 163-169.

Langhorne, P.J. and Robinson, W.H. (1986) Alignment of crystals in sea ice due to fluid motion. Cold Regions Science and Technology 12, 197-214.

Lewis, E.L. and Walker, E.R. (1970) The water structure under a growing sea ice sheet. Journal of Geophysical Research 75, 6836-6845.

Lighthill, M.J. (1978) Waves in Fluids. Cambridge University Press, Cambridge, Eng­land.

Lindgren, S. and Neumann, J. (1982) Crossings of ice-bound sea surfaces in history. Climate Change 4, 71-97.

Livesley, R.K. (1953) Some notes on the mathematical theory of a loaded elastic plate resting on an elastic foundation. Quarterly Journal of Mechanics and Applied Math­ematics 6, 32-44.

Lorch, W. (1977) Snow Travel and Transport. The Story of Snowmobility in Pictures. The Gawsworth Series, Macclesfield, England.

Love, A.E.H. (1944) A Treatise on the Mathematical Theory of Elasticity. Dover, New York, U.S.A.

Ludwig, K. (1938) Die Verformung eines beiderseits unbegrenzten elastisch gebet­teten Geleises durch Lasten mit konstanter Horizontalgeschwindigkeit. Proceedings of the Fifth International Congress of Applied Mechanics, Cambridge, Massachusetts, U.S.A., 650-655.

Malmgren, F. (1927) On the properties of sea ice. In The Norwegian North Polar Expe­dition with the "Maud" 1918-19291, ed. H.U. Sverdrup, Geofysisk Institutt, Bergen, Norway, 1-67.

218 BIBLIOGRAPHY

Martin, S. (1979) A field study of brine drainage and oil entrapment in first-year sea ice. Journal of Glaciology 22, 473~502.

Martin, S. (1981) F'razil ice in rivers and lakes. Annual Reviews of Fluid Mechanics 13, 379~397.

Masterton, D.M., Baudais, D.J., Pare, A. and Bourns, M. (1987) Drilling of a well from a sprayed floating ice platform Cape Allison C-47. Proceedings of the Sixth Interna­tional Offshore Mechanics and Arctic Engineering Symposium 4, American Society of Mechanical Engineers, Houston, U.S.A., 9~16.

Mathews, P.M. (1958) Vibrations of a beam on elastic foundation 1. Zeitschrift fur Ange­wandte Mathematik und Mechanik 38, 105~115.

Mathews, P.M. (1959) Vibrations of a beam on elastic foundation II. Zeitschrift fur Angewandte Mathematik und Mechanik 39, 13~19.

Mellor, M. (1983) Mechanical behaviour of sea ice. CRREL Monograph 83-1, Cold Re­gions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A.

Michel, B. and Ramseier, R. O. (1971) Classification of river and lake ice. Canadian Geotechnical Journal 8, 36~45.

Michel, B. (1978) Ice Mechanics. Les Presses de l'Universite Laval, Quebec, Canada. Milinazzo, F., Shinbrot, M. and Evans, N.W. (1995) A mathematical analysis of the

steady response of floating ice to the uniform motion of a rectangular load. Journal of Fluid Mechanics 287, 173~197.

Mills, D.A. (1972) On waves in a sea ice cover. Horace Lamb Centre for Oceanographic Research Report 53, Flinders University, South Australia.

Mindlin, R.D. (1951) Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Journal Applied Mechanics 18, 31~38.

Muguruma, J. and Kikuchi, K. (1963) Lake ice investigation at Peter's Lake, Alaska. Journal of Glaciology 4, 689~708.

Muravskii, G.B. (1962) Nonsteady vibrations of a beam on an elastic base when subjected to a moving load (in Russian). Izvestiya Akademii Nauk S.S.S.R., Otd. Tekh. Nauk, Mekhanika i Mashinostroenie 1, 91-97.

Nakawo, M. and Sinha, N.K. (1981) Growth rate and salinity profile of first year sea ice in the high Arctic. Journal of Glaciology 27, 315~330.

Neidrauer, T and Martin, S. (1979) An experimental study of brine drainage and con­vection in young sea ice. Journal of Geophysical Research 84, 1176~ 1186.

Nevel, D.E. (1966) Time-dependent deflection of a floating ice sheet. CRREL Research Report 196, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A.

Nevel, D.E. (1970a) Moving loads on a floating ice sheet. CRREL Research Report 261, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A.

Nevel, D.E. (1970b) Vibration of a floating ice-sheet. CRREL Research Report 281, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A.

Oldroyd, J .G. (1950) On the formulation ofthe rheological equations of state. Proceedings of the Royal Society of London, A 200, 523-541.

Paige, R. A. (1966) Crystallographic studies in McMurdo Sound, Antarctica. U.S. Naval Civil Engineering Laboratory Technical Report R494, Port Hueneme, California, U.S.A.

Perey, F.G.L. and Pounder, E.R. (1958) Crystal orientation in ice sheets. Canadian Jour­nal of Physics 36, 494-502.

Peyton, H.R. (1966) Sea ice strength. Final Report for the Department of the Navy, U.S. Office of Naval Research, Geophysical Institute of the University of Alaska, Fairbanks, Alaska, U.S.A.

Peyton, H.R. (1968) Sea-ice strength - effect of load rates and salt reinforcement. In Arctic Drifting Stations, ed. J.E. Slater, Arctic Institute of North America, Monteal, Canada, 197-216.

Peyton, H.R. (1963) Some mechanical properties of sea ice. In Ice and Snow, Proper-

BIBLIOGRAPHY 219

ties, Processes and Applications, ed. W.D. Kingery, M.LT. Press, Cambridge, Mas­sachusetts, U.S.A., 107-113.

Premachandran, R. and Horii, H. (1994) A micromechanics-based constitutive model of polycrystalline ice and FEM analysis for prediction of ice forces. Cold Regions Science and Technology 23, 19-39.

Rayner, G. (1995) Moving loads on sea ice. M.Sc. thesis, University of Otago, New Zealand.

Rayleigh, J.W.S. (1877) On Progressive waves. Proceedings of the London Mathematical Society 9, 21-26.

Rayleigh, J.W.S. (1896) Theory of Sound. Volume II, Dover, New York, U.S.A. Reissner, E. (1945) The effect of transverse shear deformation on the bending of elastic

plates. Transactions of the American Society of Mechanical Engineers 61 A, 69-77. Richter-Menge, J.A. (1992) US research in ice mechanics. Cold Regions Science and

Technology 20, 231-246. Rutter, J.W. and Chalmers, B. (1953) A prismatic substructure formed during the so­

lidification of metals. Canadian Journal of Physics 31, 15-39. Ryazanova, M. Ya. and Filonenko, G.G. (1965) Vibration of an infinite beam on an elastic

foundation subjected to a moving load taking into consideration the dissipation of energy (in Russian). Prikladnaya Mekhanika 1-8, 128-130.

Sabodash, P.F. and Filippov, LG. (1967) On a dynamic problem for a thin elastic plate (in Russian). Prikladnaya Mekhanika 111-6, 48-53.

Saito, T. and Ono, N. (1980) Percolation of sea ice II - Brine drainage channels in young sea ice. Low Temperature Science A 39, 127-132.

Sanderson, T.J.O. (1988) Ice Mechanics: Risks to Offshore Structures. Graham & Trot­man, London, U.K.

Santaoja, K (1989) Continuum damage mechanics approach to describe the multidirec­tional microcracking of ice. Proceedings of the Eighth International Offshore Mechan­ics and Arctic Engineering Symposium 4, American Society of Mechanical Engineers, Den Hague, Holland, 55-65.

Schleicher, F. (1926) Kreisplatten auf Elastischer Unterlage. Springer, Berlin, Germany. Schulkes, R.M.S.M., Hosking, R.J. and Sneyd, A.D. (1987) Waves due to a steadily

moving source on a floating ice plate. Part 2. Journal of Fluid Mechanics 180, 297-318.

Schulkes, R.M.S.M. and Sneyd, A.D. (1988) Time-dependent response of a floating ice sheet to a steadily moving load. Journal of Fluid Mechanics 186, 25-46.

Schwarz, J., Frederking, R., Gavrillo, V., Petrov, LG., Hirayama, K.-I, Tryde, P. and Vau­drey, KD. (1981) Standardised testing methods for measuring mechanical properties of ice. Cold Regions Science and Technology 4, 245-253.

Shyam Sunder, S. and Wu, M.S. (1989) A multiaxial differential model of low in or­thotropic polycrystalline ice. Cold Regions Science and Technology 16, 223-236.

Shyam Sunder, S. and Wu, M.S. (1990) On the constitutive modeling of transient creep in polycrystalline ice. Cold Regions Science and Technology 18, 267-294.

Sinha, N.K (1977) Technique for studying structure of sea ice. Journal of Glaciology 18, 315-323.

Sinha, N.K (1978) Short-term rheology of polycrystalline ice. Journal of Glaciology 21, 457-473.

Sinha, N.K (1979) Grain boundary sliding in polycrystalline materials. Philosophical Magazine A 40, 825-842.

Sinha, N.K (1987) Dislocation climb in ice observed by etching and replicating. Journal of Material Science Letters 6, 1406-1408.

Sinha, N.K (1988) Crack-enhanced creep in polycrystalline material: strain-rate sensitive strength and deformation of ice. Journal of Materials Science 23, 4415-4428.

Sinha, N.K (1990) Crowd induced deflection of Dow's Lake ice cover during Winterlude Festival 1985. Proceedings of the Ninth International Offshore Mechanics and Arc­tic Engineering Symposium 4 American Society of Mechanical Engineers, Houston,

220 BIBLIOGRAPHY

U.S.A., 161-167. Sinha, N.K. (1991) Cracking kinetics and failure on repeated loadings of ice. International

Symposium on Fatigue and Fracture in Steel and Concrete Structures, Madras, India, 137-150.

Sinha, N.K. (1992) Winterlude 1986 - Dow's Lake ice loading test. Proceedings of the Eleventh International Offshore Mechanics and Arctic Engineering Symposium 4 American Society of Mechanical Engineers, Calgary, Canada, 303-310.

Sinha, N.K. (1995) Sea ice landing strip for Boeing-727 in northern Greenland. Pro­ceedings of the Fourteenth International Offshore Mechanics and Arctic Engineering Symposium 4 American Society of Mechanical Engineers, Copenhagen, Denmark, 273-279.

Sjolind, S.G. (1987) A constitutive model for ice as a damaging visco-elastic material. Cold Regions Science and Technology 14, 247-262.

Sokolnikoff (1956) Mathematical Theory of Elasticity. McGraw-Hill, New York, U.S.A. Squire, V.A. (1986) Wind over ice: a mechanism for the generation of ice-coupled waves.

In Ice Technology, ed. T.K.S. Murthy et al., Springer-Verlag, New York, U.S.A., 115-128.

Squire, V.A. and Allan, A.J. (1980) Propagation of flexural gravity waves in sea ice. In Sea Ice Processes and Models, ed. R.S. Pritchard, University of Washington Press, Seattle, U.S.A., 327-338.

Squire, V.A., Langhorne, P.J., Robinson, W.H. and Heine, A.J. (1986) Kiwi 131: an Antarctic field experiment to study strains and acoustic emission generated by loads moving over sea ice. Report prepared for the Royal Society of London.

Squire, V.A., Robinson, W.H., Haskell, T.G. and Moore, S.C. (1985) Dynamic strain response of lake and sea ice to moving loads. Cold Regions Science and Technology 11,123-139.

Squire, V.A., Robinson, W.H., Langhorne, P.J. and Haskell, T.G. (1988) Vehicles and aircraft on floating ice. Nature (London) 333, 159-161.

Stander, E. and Michel, B. (1990) The effect of fluid flow on the development of preferred orientations in sea ice: laboratory experiments. Cold Regions Science and Technology 17, 153-162.

Steele, C.R. (1967a) The finite beam with a moving load. Journal of Applied Mechanics, 34,111-118.

Steele, C.R. (1967b) Nonlinear effects in the problem of the beam on a foundation with a moving load. International Journal of Solids and Structures 3, 565-585.

Steele, C.R. (1968) The Timoshenko beam with a moving load. Journal of Applied Me­chanics 35, 481-488.

Steele, C.R. (1971) Beams and shells with moving loads. International Journal of Solids and Structures 7,1171-1198.

Strathdee, J., Robinson, W.H. and Haines, E.M. (1991) Moving loads on ice plates of finite thickness. Journal of Fluid Mechanics 226, 37-61.

Sunberg-Falkenmark, M. (1963) Resultat av belastningsfOrsok pa is, utforda av Samar­betsgruppen fOr isbiirighetsforsok 1959-61 (in Swedish). Notiser Och Preliminiira Rapporter, Serie Hydrologi 1, Sveriges Meteorologiska och Hydrologiska Institut, Stockholm, Sweden.

Swamidas, A.S.J., EI-Tahan, H. and Reddy, D.V. (1979) Proceedings of the Workshop on the Bearing Capacity of Ice Covers, ed. R. Frederking, Technical Memorandum 123, National Research Council, Canada, 183-203.

Szyszkowski, W. and Glockner, P.G. (1985) Modelling the time-dependent behaviour of ice. Cold Regions Science and Technology 11, 3-21.

Tabata, T. (1959) Studies of the mechanical properties of sea ice IV (in Japanese). Low Temperature Science A 18, 131-148.

Takizawa, T. (1978) Deflection of a floating ice sheet subjected to a moving load II (in Japanese). Low Temperature Science A 37, 69-78.

Takizawa, T. (1985) Deflection of a floating sea ice sheet induced by a moving load. Cold

BIBLIOGRAPHY 221

Regions Science and Technology 11,171-180. Takizawa, T. (1987) Field studies on response of a floating sea ice sheet to a steadily

moving load. Contributions from the Institute of Low Temperature Science A 36, 31-76.

Takizawa, T. (1988) Response of a floating sea ice sheet to a steadily moving load. Journal of Geophysical Research 93, 5100-5112.

Tang, S.C. and Yen, D.H.Y. (1970) A note on the nonlinear response of an elastic beam on a foundation to a moving load. International Journal of Solids and Structures 6, 1451-1461.

Thomson, W. (1871) Hydrokinetic solutions and observations. Philosophical Magazine XLII, 362-377.

Timoshenko, S.P. (1921) On the correction for shear of the differential equation for trans­verse vibrations of prismatic bars. Philosophical Magazine 41, 744-746. (See also collected papers, 288-290.)

Timoshenko, S. (1927) Method of analysis of statical and dynamical stresses in rail. Proceedings of the Second International Congress of Applied Mechanics, Zurich, 1-12. (See also collected papers, 422-435.)

Timoshenko, S. and Woinowsky-Krieger, S. (1959) Theory of Plates and Shells. 2nd ed., McGraw-Hill, New York, U.S.A.

Traetteberg, A., Gold, L.W and Frederking, R. (1975) The strain rate and tempera­ture dependence of Young's modulus of ice. Proceedings of the Third International Symposium on Ice Problems, Hanover, New Hampshire, U.S.A., 479-486.

Uflyand, Y.S. (1948) The propagation of waves in the transverse vibrations of bars and plates (in Russian). Akad. Nauk S.S.S.R., Prikladnaya Matematika i Mekhanika 12, 287-300.

Untersteiner, N. (1967) Natural desalination and equilibrium salinity profile of old sea ice. In Physics of Snow and Ice, ed. H. Oura, Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan, 569-577.

Wadhams, P. (1990) Ice thickness distribution in the Arctic Ocean. In Ice Technology for Polar Operations, ed. T.K.S. Murthy et al., Computational Mechanics Publications, England, 3-20.

Wakatsuchi, M. and Saito, T. (1985) On the brine drainage channels of young sea ice. Annals of Glaciology 6, 200-202.

Wakatsuchi, M. and Kawamura, T. (1987) Formation processes of brine drainage channels in sea ice. Journal of Geophysical Research 92, 7195-7197.

Walker, E.R. and Wadhams, P. (1979) Thick sea-ice floes. Arctic 32,140-147. Walters, K. (1975) Rheometry. Chapman and Hall, London, England. Weeks, W.F. (1958) The structure of sea ice: a progress report. In Arctic Sea Ice, Publi­

cation 598, National Academy of Sciences - National Research Council, Washington D.C., U.S.A., 96-99.

Weeks, W.F. and Ackley, S.F. (1982) Growth, structure and properties of sea ice. CRREL Monograph 82-1, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A.

Weeks, W.F. and Assur, A. (1967) The mechanical properties of sea ice. Cold Regions Re­search and Engineering II-C3, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A.

Weeks, W.F. and Gow, A.J. (1978) Preferred crystal orientations along the margins of the Arctic Ocean. Journal of Geophysical Research 83, 5105-5121.

Weeks, W.F. and Gow A.J. (1980) Crystal alignments in the fast ice of Arctic Alaska. Journal of Geophysical Research 85, 1137-1146.

Weeks, W.F. and Lee, O.S. (1958) Observations on the physical properties of sea ice in Hopedale, Labrador. Arctic 11, 135-155.

Weeks, W.F. and Lee, O.S. (1962) The salinity distribution in young sea ice. Arctic 15, 92-108.

Weeks, W.F. and Lofgren, G. (1967) The effective solute distribution coefficient during

222 BIBLIOGRAPHY

the freezing of NaCl solutions. In Physics of Snow and Ice, ed. H. Oura, Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan, 579-597.

Weeks, W.F. and Mellor, M. (1984) Mechanical properties of ice in Arctic seas. In Arctic Technology and Policy, ed. I. Dyer and C. Cryssostomidis, Hemisphere, Washington, 235-259.

Whitham, G.B. (1974) Linear and Nonlinear Waves. John Wiley & Sons, New York, U.S.A.

Whitten, J. and Hinchey, M.J. (1988) Critical speed data for model floating ice roads and runways. Canadian Aemnautics and Space Journal 34, 151-161.

Wilson, J.T. (1955) Coupling between moving loads and flexural waves in floating ice sheets. US Army SIPRE Report 34, Cold Regions Research and Engineering Labo­ratory, Hanover, New Hampshire, U.S.A.

Wilson, J.T. (1958) Moving loads on floating ice sheets. University of Michigan Research Institute Report, Project 2432, Michigan, U.S.A.

Winkler, E. (1867) Die Lehre von der Elastizitiit und Festigkeit (in German). Praga Dominicus, Germany.

Wyman, M. (1950) Deflections of an infinite plate. Canadian Journal of Research 28, 293-302.

Yen, D.H.Y. and Tang, S.C. (1970) On the nonlinear response of an elastic string to a moving load. International Journal of Non-Linear Mechanics 5, 465-474.

Yen, D.H.Y. and Tang, S.C. (1976) Nonlinear waves generated by a steadily moving line load on an elastic plate. International Journal of Solids and Structures 12, 467-477.

Zhan, C., Evgin, E. and Sinha, N.K. (1994) A three dimensional anisotropic constitu­tive model for ductile behaviour of columnar grained ice. Cold Regions Science and Technology 22, 269-284.

INDEX

abnormal resistance see wave drag accelerometer 187, 199 acoustic emissions 163 aircraft 211

Boeing-727 4, 5, 39 C-47 161, 162 C-131 162 LC-130 Hercules 164,179,211

amplification factor 206ff dependence on temperature 207 field estimates of 160-171 pas­

sim, 178, 180-182 table of values 208

aspect ratio 121 axial forces see in-plane forces

base elastic see Winkler base fluid see fluid base inertia 70, 77, 93 Winkler see Winkler base

beam see elastic beam, thick, on Winkler base and elastic beam, thin, on Winkler base

bearing capacity 2, 4-6, 39, 60, 206

bending force 59, 60, 106 bending theory 57, 69 Bernoulli-Love hypothesis 53 Bernoulli (pressure) condition see

boundary conditions blowout 4 boundary conditions

bottom (lake or sea floor) 65, 105

surface

223

kinematic (noncavitation) 65-67, 105, 107, 147

ice see ice plate, various pressure (Bernoulli) 64, 65,

67, 147 bulk modulus, relationship to Lame

constants 51

caustic 113, 114-116, 145, 184 characteristic length

dynamic 156 static 91, 163, 166, 167, 170,

180, 190 compatibility condition 49 critical speed

elastic beam, thick, on Win­kler base 87

elastic beam, thin, on Win­kler base 72, 75, 77-84

with in-plane forces 84, 85 elastic plate, thin, on Winkler

base 89,90 free surface with surface ten­

sion 100, 101 ice plate, elastic, thin 93, 95,

96, 98, 99, 107-111 pas­sim, 114-121 passim, 121-130 passim, 132, 133, 200ff

density of ice, effect on 202, 203

density of water, effect on 202, 203

field estimates of 160ff ice thickness, effect on 201,

203-206

224 INDEX

in-plane forces, effect on 203, 204

Poisson's ratio, effect on 201, 203

water depth, effect on 202-204

Young's modulus, effect on 201, 203-206

ice plate, viscoelastic, thin 137-139, 143

viscosity, effect on 203, 204 critical wave number see critical

speed critical wavelength see critical speed current under ice 25, 86, 203 cusp 114-116, 118

dead water see wave drag deflectometer 160-176 passim deflexion see steady ice deflexion,

elastic and steady ice de­flexion, viscoelastic

deflexion or strain variation with speed see also amplifica­tion factor

deflexion or strain variation with speed 78, 143, 170, 175, 182

density ice, variation 202 water, variation 202

depression see also steady ice de­flexion, elastic and steady ice deflexion, viscoelastic

depression depth 170, 171, 175 width 170, 171, 174, 176

dispersion relation elastic beam, thin, on Win­

kler base 71, 72 elastic plate, thin, on Winkler

base 88 ice free (open water) 66, 108

ice plate, elastic, thin stratified fluid base 147-149 unstratified fluid base 96, 106-

109, 111, 112, 117, 122, 131, 170, 178, 180, 200, 203

ice plate, viscoelastic, thin 137, 138

wave number curve 112 disturbance front 129, 130

elastic beam, thick, on Winkler base 86ff

elastic beam, thin, on Winkler base 70ff

damped 80-84 basic equation 81 deflexion, due to moving load

82,83 qualitative synopsis 82, 83 transformed equation 82

undamped 70-80 basic equation 71 deflexion, due to moving load

75-77, 79-83 transformed equation 73, 74

with in-plane forces see in-plane forces

elasticity delayed, anelastic see also me­

chanical properties, ice delayed, anelastic 33-38, 41-

43,48,134-136,139,173, 204, 207, 209

instantaneous, Hookean 48ff base see Winkler base constitutive relation 50 moduli 50 solid, definition 47, 48

elastic plate, thin 52ff homogeneous equation 56 inhomogeneous equation 58

Rayleigh, with rotatory iner­tia 56

INDEX

with in-plane forces see in-plane forces

elastic plate, thin, floating see ice plate, elastic, thin

elastic plate, thin, on Winkler base 88ff

anisotropic 90 basic equation 88

energy accumulation 110, 111 experiments

field 159ff qualitative synopsis of results

163, 165, 168-170, 177 laboratory 159, 176-178

flexural rigidity see rigidity, flex­ural and bending

floating ice plate see ice plate, elas­tic, thin and ice plate, vis­coelastic, thin and ice plate, viscoelastic, of finite thick­ness

fluid 48 deflexion of surface by moving

line load 99ff fluid base (foundation) 61ff

Bernoulli's pressure equation 64, 65, 67

constitutive relation 63, 64 continuity equation 62 deep 96, 98, 99, 107, 108, 163,

178,181-183 Euler's equation 63 Laplace's equation 64,67, 105 Navier-Stokes equations 63 stratified 145ff

foundation elastic see Winkler base fluid see fluid base Winkler see Winkler base

225

Fourier transform 77-90 passzm, 94,96, 97, 111, 117, 122, 131,134-140 passim, 151, 152, 156

free surface waves 64ff boundary conditions 65 dispersion relation 65

freshwater ice 1-4 passim, 29ff, 48, 57, 59, 68, 133, 159-165 passim, 178, 206, 211

growth 31ff frazil ice 31 geometric selection 31

mechanical properties see me­chanical properties, ice

structural features c-axis see also ice c-axis 31, 32 columnar ice 31 grain size 30, 31 ice-water interface 29, 30 impurities 30 liquidus 30 primary ice 31

gravity wave speed JgH, limiting 107, 108, 110, 111, 115, 117,118,121-130 passim, 134

group speed 72, 77, 80, 89, 99, 107-110,123, 128-130, 149, 150, 157

historical ice crossings 1 Gulf of Finland 1 Sea of Azov 1 trains 1-3

Lake Baikal 2 Lake Ladoga 93, 160 St Lawrence River 2 Sungari River, Manchuria 2,

159, 160 Trans-Canada railroad 2

226

Trans-Siberian railway 1 homologous temperature 33, 34,

150 Hooke's law

generalized 50, 51 uniaxial 39

hump speed see also critical speed hump speed 4

ice, atomic structure 9ff a-axis, definition 10 Bernal-Fowler rules 10 c-axis, definition 10 defects 10 hydrogen and oxygen atoms

10 ice forms 9

INDEX

ice, freshwater see freshwater ice ice plate, elastic, thin 66-68, 90ff,

105-133,146-149, 154-157 basic equations 66,67,93,105 deflexion, due to stationary load

90-92 concentrated point load 91 distributed load 91-92

steady de flexion due to mov­ing load see steady ice de­flexion, elastic

steady strain due to moving load 189

unsteady deflexion due to mov­ing load see unsteady ice deflexion, elastic

vibrating load see vibrating load ice plate, viscoelastic, of finite thick-

ness 150ff asymptotic solutions 152, 153 basic equations 151, 152 strains, formal 152

ice plate, viscoelastic, thin 67, 68, 133ff

basic equations 59-60, 68, 135, 136

with in-plane forces 199 steady deflexion due to mov­

ing load see steady ice de­flexion, viscoelastic

ice, sea see sea ice inhomogeneity 56ff in-plane forces 74,84-86,90, 131,

133, 134, 199, 203, 204

kinematic (noncavitation) condi­tion see boundary condi­tions

Kirchhoff's hypothesis 53 Kronecker delta 51

lag between load and largest de­flexion 163, 167-174

time 173,174 lake floor condition see boundary

conditions lake ice see freshwater ice load

concentrated see steady ice de­flexion, elastic and steady ice deflexion, viscoelastic

distributed see steady ice de­flexion, elastic and steady ice de flexion , viscoelastic and unsteady ice deflex­ion, elastic

impulsively-started see unsteady ice deflexion, elastic

line see steady ice de flexion , elastic and steady ice de­flexion, viscoelastic and un­steady ice deflexion, elas­tic

stationary see ice plate, elas­tic, thin

vibrating see vibrating load Lupin gold mine, Canada 4

material description 47

INDEX

Eulerian 47, 48, 50 Lagrangian 47, 52

mathematical model, simplest ac­ceptable 52,66, 70,81, 105, 110, 130, 150, 157, 158

mechanical properties, ice 33ff activation energy 42 anelasticity see elasticity, de­

layed cracks and crack density 36-

38 creep see also viscosity, irrecov­

erable creep 34-38, 42, 134, 136, 160

constant load test 34 steady state 34 tertiary 34, 35, 136

dislocations 10, 39, 41, 42 elasticity, delayed 33-39, 41-

43 grain boundary relaxation 41 grain boundary sliding 37,

41,42 elasticity, instantaneous 33-41,

43 hysteresis see also inelasticity hysteresis 166, 182, 193 inelasticity 33, 34, 43, 68, 70,

105, 114, 133, 150, 163, 166, 171, 196, 199, 206, 207, 209

internal friction 173 microcracks 34, 36 thermodynamic and microme-

chanical 35, 36 viscosity, irrecoverable 34-38,

43, viscosity, recoverable see also

elasticity, delayed viscosity, recoverable 34

moments bending 55, 56

twisting 55, 56 momentum equation 50

elastic plate 54, 55

227

moving reference frame 73, 89, 117, 122, 131, 137, 156

neutral surface 58

phase speed 71-73,75,89,99-101, 107-110,112,115,118,123, 126, 129, 137, 149, 150

minimum see critical speed physical parameters 67, 105 plate acceleration, neglect of 107,

111, 122, 123, 136, 148, 149, 200, 201

plate of finite thickness 60ff, 68 floating see ice plate, viscoelas­

tic, of finite thickness Poisson's ratio, variation 41, 57,

201, 203 relationship to Lame constants

51 portage 4 pressure (Bernoulli) condition see

boundary conditions

resonance equation, damped 160 response

classification scheme 163, 165, 168, 170, 175-177, 180

evolving see unsteady ice de­flexion, elastic

lag see lag between load and largest deflexion

steady state see steady ice de­flexion, elastic and steady ice deflexion, viscoelastic

transients 73, 78, 79, 86, 87, 89,99,110,124,126-130, 132

rigidity, flexural and bending

228

homogeneous 56, 71, 73, 88, 90

INDEX

from critical speed 204~206 partially relaxed 153

inhomogeneous 58, 59, 67 partially relaxed 137, 148,

179, 180, 199~201,206,207 river ice see freshwater ice rotatory inertia see elastic plate,

thin

sea floor condition see boundary conditions

sea ice 1, 4, 5, 9ff, 48, 57, 59, 67, 86, 136, 146, 150, 162, 164, 178, 179, 193, 196, 201, 205~208 passim, 211

brine content and desalination 26~29

brine drainage channel 19~ 21, 27~29

brine expulsion 26 brine pocket 17~19, 26, 29,

30, 33, 40, 42 brine pocket migration 26 brine volume 26~29 flushing 26, 28 gravity drainage 27 salinity and salinity profile 9~ 15 passim, 19, 26ff, 28, 29,39

c-axis see also ice c-axis 10, 16, 18, 20~24, 25ff,

44 convection 15, 20 gas content see also brine con­

tent and desalination gas content 28~ 29 growth 20ff

geometric selection 22~24 solute entrapment 26

macroscopic features and types congelation ice 12

first year ice 12 frazil ice 21 grease ice 10 land fast ice see shore fast

Ice lead 10, 11 multiyear ice 12 pack ice 12 pancake ice 10, 13 polynya 11 pressure ridge 12 rafting 11 rubble field 12 shore fast ice 12, 86, 178,

209 mechanical properties see me­

chanical properties, ice phase diagram see brine con­

tent and desalination structural features

bottom ice 25 columnar zone 24, 25 grain size 19, 22, 24, 25 ice-water interface 12, 15~

18, 22, 25, 26, 43 infiltrated snow ice 22 liquidus 15, 16 orientation of c-axes see c-

axis platelets 16~ 19, 36 skeletal layer 15~ 18, 20, 26 supercooled layer 21 transition layer 22, 24

sea water see water shear, transverse see also ice plate,

viscoelastic, of finite thick­ness

shear, transverse 55, 69, 86, 87 shearing forces, large scale 11 steady ice deflexion, elastic

concentrated point load 93, 96, 97

INDEX

distributed load 97, 98, 111ff, 117-121

asymptotic solution 113, 114, 118, 189

numerical solution 118 shadow zone 115-118, 129,

169, 180 wave crest patterns 114-121,

185-187 width of depression 170, 171,

174,176 line load 93-96

part of unsteady solution 124-126 passim, 132

steady ice deflexion, viscoelastic 135ff, 150ff

concentrated point load 142 distributed load 141

asymptotic solution 144 wave patterns 145, 146

Green's functions 152, 153 line load 137-141

strain bulk 51 definition 49 deviatoric 51 plane 52 principal, angle of 187-195 principal, maximum and min-

imum 187-195 rate of 33-45 passim, 49

strain gauge 164, 165, 177, 180-190 passim

strain gauge rosette 187ff four-gauge 45° fan 187, 188 three-gauge 45° star 187, 188

stress bulk 51 definition 48-49 deviatoric 51 inhomogeneous plate 59 intergranular shear 41

multi axial 34, 36 plane 52 resultant 55 uniaxial 34, 37

supercaustic 114-116 surface tension 99ff

tandem vehicle tests 160, 161 tensor, Cartesian 47

deformation gradient 49 strain see strain

229

strain rate see strain, rate of stress see stress

thin elastic plate see elastic plate, thin

thin viscoelastic plate see ice plate, viscoelastic, thin

unsteady ice deflexion, elastic distributed load 130ff line load 99, 121ff

leading to steady state 124-126, 128, 129

not leading to steady state 127, 129, 130

shadow zone 126

vibrating load 154ff viscoelastic 48, 59ff, 133ff

anelastic 33, 37, 41, 42, 48, 134-136,141,158,172,203, 204, 207, 209

bending force 59 Burger's unit 134 creep 34-38, 42, 59, 60, 90,

134-136,160,172,203,207 decay (damping) factor 138,

144, 145, 162, 209 hereditary integral 59, 60, 136,

158, 199 Maxwell unit 134-136, 139, 172 memory function 59, 60, 136,

141, 200

230

phase factor 138 solid, definition 47, 48 standard model 136

INDEX

Voigt unit 134, 136, 139, 141 viscoelastic plate, thin, floating see

ice plate, viscoelastic, thin viscous damping see also mechan­

ical properties, ice viscous damping 80ff, 103, 133, 135,

141, 150, 152, 161, 162, 171, 172, 204

memory function see viscoelas­tic

water see also fluid base water

fresh impurities 30 supercooling 31

sea 12, 14 constitutional supercooling

16 impurities 14, 26 salts 14, 19, 28 salts, effect on freezing point

14 salts, effect on temperature

of maximum density 14 temperature of maximum den­

sity 14, 29, 30 wave crest 112, 114-116, 126, 134,

144-146,166,175,177,178, 182, 184-187, 189, 193

wave drag 149, 158 wave number curve see also dis­

persion relation wave number curve 112, 181-183 wave pattern, steady state 111-

113, 114ff, 119-121, 126, 133, 135, 142, 144

waves development 105, 118, 129 far field 209ff

free plane 65,71,88,105-107, 147

free surface see free surface waves hybrid 72, 73, 100, 106-108,

137, 145, 149 internal 145, 146, 148, 149, 158 modulation time scale 124 shadow zone 115-118, 126, 129,

169, 180 surface flexural-gravity

short leading, long trailing 72,78-80,83,99,100,109, 114, 126, 128, 129, 139, 144, 163, 166, 170, 178, 180,185-187,190-196,209

wave train 71, 78, 79, 80, 82, 88, 89, 100, 103, 126, 128, 129

Winkler base (foundation) 52, 61, 62, 70-72, 73-92 passim, 101, 106, 110, 131, 171

x-ray crystallography 9

Young's modulus effective see partially relaxed high frequency 39, 40, 43, 45,

162, 179 inhomogeneous plate 57, 179 partially relaxed 43ff, 48, 56,

179 from critical speed 204-206

relationship to Lame constants 51

Mechanics

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A Modern Course in Aeroelasticity. Third Revised and Enlarged Edition. 1995 ISBN 0-7923-2788-8; Pb: 0-7923-2789-6

33. A. Preumont: Random Vibration and Spectral Analysis. 1994 ISBN 0-7923-3036-6 34. J.N. Reddy (ed.): Mechanics of Composite Materials. Selected works of Nicholas J. Pagano.

1994 ISBN 0-7923-3041-2 35. A.P.S. Selvadurai (ed.): Mechanics of Poroelastic Media. 1996 ISBN 0-7923-3329-2 36. Z. Mr6z, D. Weichert, S. Dorosz (eds.): Inelastic Behaviour of Structures under Variable

Loads. 1995 ISBN 0-7923-3397-7 37. R. Pyrz (ed.): IUTAM Symposium on Microstructure-Property Interactions in Composite

Materials. Proceedings of the IUT AM Symposium held in Aalborg, Denmark. 1995 ISBN 0-7923-3427-2

38. M.I. Friswell and J.E. Mottershead: Finite Element Model Updating in Structural Dynamics. 1995 ISBN 0-7923-3431-0

39. D.F. Parker and A.H. England (eds.): IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics. Proceedings of the IUTAM Symposium held in Nottingham, U.K. 1995 ISBN 0-7923-3594-5

40. I.-P. Merlet and B. Ravani (eds.): Computational Kinematics '95. 1995 ISBN 0-7923-3673-9 41. L.P. Lebedev, 1.1. Vorovich and G.M.L. Gladwell: Functional Analysis. Applications in

Mechanics and Inverse Problems. 1996 ISBN 0-7923-3849-9 42. I. Mencik: Mechanics of Components with Treated or Coated Surfaces. 1996

ISBN 0-7923-3700-X 43. D. Bestle and W. Schiehlen (eds.): IUTAM Symposium on Optimization of Mechanical

Systems. Proceedings of the IUT AM Symposium held in Stuttgart, Germany. 1996 ISBN 0-7923-3830-8

Kluwer Academic Publishers - Dordrecht / Boston / London

Mechanics SOLID MECHANICS AND ITS APPLICATIONS

Series Editor: G.M.L. Gladwell

44. D.A. Hills, P.A. Kelly, D.N. Dai and A.M. Korsunsky: Solution of Crack Problems. The Distributed Dislocation Technique. 1996 ISBN 0-7923-3848-0

45. V.A. Squire, R.I. Hosking, A.D. Kerr and P.I. Langhorne: Moving Loads on Ice Plates. 1996 ISBN 0-7923-3953-3

Kluwer Academic Publishers - Dordrecht / Boston / London

Mechanics

From 1990, books on the subject of mechanics will be published under two series: FLUID MECHANICS AND ITS APPLICA nONS

Series Editor: R.I. Moreau SOLID MECHANICS AND ITS APPLICA nONS

Series Editor: G.M.L. Gladwell

Prior to 1990, the books listed below were published in the respective series indicated below.

MECHANICS: DYNAMICAL SYSTEMS

Editors: L. Meirovitch and G.lE. Oravas

1. E.H. Dowell: Aeroelasticity of Plates and Shells. 1975 ISBN 90-286-0404-9 2. D.G.B. Edelen: Lagrangian Mechanics of Nonconservative Nonholonomic Systems.

1977 ISBN 90-286-0077-9 3. J.L. Junkins: An Introduction to Optimal Estimation of Dynamical Systems. 1978

ISBN 90-286-0067-1 4. E.H. Dowell (ed.), H.C. Curtiss Jr., R.H. Scanlan and F. Sisto: A Modern Course in

Aeroelasticity. Revised and enlarged edition see under Volume 11 5. L. Meirovitch: Computational Methods in Structural Dynamics. 1980

ISBN 90-286-0580-0 6. B. Skalmierski and A. Tylikowski: Stochastic Processes in Dynamics. Revised and

enlarged translation. 1982 ISBN 90-247-2686-7 7. P.C. MUller and W.O. Schiehlen: Linear Vibrations. A Theoretical Treatment of Multi-

degree-of-freedom Vibrating Systems. 1985 ISBN 90-247-2983-1 8. Gh. Buzdugan, E. Mihailescu and M. Rade§: Vibration Measurement. 1986

ISBN 90-247-3111-9 9. G.M.L. Gladwell: Inverse Problems in Vibration. 1987 ISBN 90-247-3408-8

10. G.I. Schueller and M. Shinozuka: Stochastic Methods in Structural Dynamics. 1987 ISBN 90-247-3611-0

11. E.H. Dowell (ed.), H.C. Curtiss Jr., R.H. Scanlan and F. Sisto: A Modern Course in Aeroelasticity. Second revised and enlarged edition (of Volume 4). 1989

ISBN Hb 0-7923-0062-9; Pb 0-7923-0185-4 12. W. Szemplirlska-Stupnicka: The Behavior of Nonlinear Vibrating Systems. Volume I:

Fundamental Concepts and Methods: Applications to Single-Degree-of-Freedom Systems. 1990 ISBN 0-7923-0368-7

13. W. Szemplmska-Stupnicka: The Behavior of Nonlinear Vibrating Systems. Volume II: Advanced Concepts and Applications to Multi-Degree-of-Freedom Systems. 1990

ISBN 0-7923-0369-5 Set ISBN (Vols. 12-13) 0-7923-0370-9

MECHANICS OF STRUCTURAL SYSTEMS

Editors: 1.S. Przemieniecki and G.lE. Oravas

1. L. Fryba: Vibration of Solids and Structures under Moving Loads. 1970 ISBN 90-01-32420-2

2. K. Marguerre and K. W6lfel: Mechanics of Vibration. 1979 ISBN 90-286-0086-8

Mechanics 3. E.B. Magrab: Vibrations of Elastic Structural Members. 1979 ISBN 90-286-0207-0 4. R.T. Haftka and M.P. Kamat: Elements of Structural Optimization. 1985

Revised and enlarged edition see under Solid Mechanics and Its Applications, Volume 1 5. J.R. Vinson and R.L. Sierakowski: The Behavior of Structures Composed of Composite

Materials. 1986 ISBN Hb 90-247-3125-9; Pb 90-247-3578-5 6. RE. Gatewood: Virtual Principles in Aircraft Structures. Volume 1: Analysis. 1989

ISBN 90-247-3754-0 7. B.E. Gatewood: Virtual Principles in Aircraft Structures. Volume 2: Design, Plates,

Finite Elements. 1989 ISBN 90-247-3755-9 Set (Gatewood 1 + 2) ISBN 90-247-3753-2

MECHANICS OF ELASTIC AND INELASTIC SOLIDS

Editors: S. Nemat-Nasser and G.1E. Oravas

1. G.M.L. Gladwell: Contact Problems in the Classical Theory of Elasticity. 1980 ISBN Hb 90-286-0440-5; Pb 90-286-0760-9

2. G. Wempner: Mechanics of Solids with Applications to Thin Bodies. 1981 ISBN 90-286-0880-X

3. T. Mura: Micromechanics of Defects in Solids. 2nd revised edition, 1987 ISBN 90-247-3343-X

4. R.G. Payton: Elastic Wave Propagation in Transversely Isotropic Media. 1983 ISBN 90-247-2843-6

5. S. Nemat-Nasser, H. Abe and S. Hirakawa (eds.): Hydraulic Fracturing and Geother-mal Energy. 1983 ISBN 90-247-2855-X

6. S. Nemat-Nasser, R.I. Asaro and G.A. Hegemier (eds.): Theoretical Foundation for Large-scale Computations of Nonlinear Material Behavior. 1984 ISBN 90-247-3092-9

7. N. Cristescu: Rock Rheology. 1988 ISBN 90-247-3660-9 8. G.I.N. Rozvany: Structural Design via Optimality Criteria. The Prager Approach to

Structural Optimization. 1989 ISBN 90-247-3613-7

MECHANICS OF SURFACE STRUCTURES

Editors: W.A. Nash and G.1E. Oravas

1. P. Seide: Small Elastic Deformations of Thin Shells. 1975 ISBN 90-286-0064-7 2. V. Panc: Theories of Elastic Plates. 1975 ISBN 90-286-0104-X 3. J.L. Nowinski: Theory ofThermoelasticity with Applications. 1978

ISBN 90-286-0457-X 4. S. Lukasiewicz: Local Loads in Plates and Shells. 1979 ISBN 90-286-0047-7 5. C. Fili: Statics, Formfinding and Dynamics of Air-supported Membrane Structures.

1983 ISBN 90-247-2672-7 6. Y. Kai-yuan (ed.): Progress in Applied Mechanics. The Chien Wei-zang Anniversary

Volume. 1987 ISBN 90-247-3249-2 7. R. Negruliu: Elastic Analysis of Slab Structures. 1987 ISBN 90-247-3367-7 8. J.R. Vinson: The Behavior of Thin Walled Structures. Beams, Plates, and Shells. 1988

ISBN Hb 90-247-3663-3; Ph 90-247-3664-1