Abstract
The present paper is concerned with the stresses produced due to a load moving on the irregular surface of an ice sheet floating on water. The irregularity of the ice medium is of parabolic type, and a rectangular irregularity has also been considered as a special case. The mathematical formulation of this physical problem gives rise to a boundary value problem with the specified boundary conditions. The perturbation method is applied to find the displacement field. Closed-form expressions of the normal and shear stresses developed in the ice medium and semi-infinite water medium due to moving load and irregularity have been derived using the boundary conditions. The variations of dimensionless normal and shear stresses with different depth below the surface are computed for a realistic numerical model and discussed. The same numerical data are used for surface plots to analyze the combined variation of non-dimensional stresses and velocity ratio against depth. From the outcome of the numerical study, the normal and shear stresses developed in both the ice and water media are found to be very sensitive to the changes in frictional coefficient, dimensionless wave number and irregularity factor present in the medium.
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References
Sato, Y.: Study on surface waves. II: velocity of surface waves propagated upon elastic plates. Bull. Earthq. Res. Inst. Univ. Tokyo 29, 223–261 (1951)
Ewing, M., Press, F.: Crustal structure and surface-wave dispersion. Bull. Seismol. Soc. Am. 40, 271–280 (1950)
Ewing, M., Press, F.: Crustal structure and surface wave dispersion. Part II: Solomon Islands Earthquake of 29 July 1950. Bull. Seismol. Soc. Am. 42, 315–325 (1951)
Anderson, D.L.: Preliminary results and review of sea ice elasticity and related studies. Trans. Eng. Inst. Can. 2, 116–122 (1958)
Bogorodoskii, V.V.: The elastic characteristics of ice. Sov. Phys. Acoust. 4, 17–21 (1958)
Sneddon, I.N.: The stress produced by a pulse of pressure moving along the surface of a semi-infinite solid. Rend. Circ. Mat. Palermo 2, 57–62 (1952)
Cole, J., Huth, J.: Stresses produced in a half-plane by moving loads. J. Appl. Mech. 25, 433–436 (1958)
Craggs, J.W.: On two dimensional waves in an elastic half-space. Math. Proc. Camb. Philos. Soc. 56(3), 269–285 (1960)
Sackman, J.L.: Uniformly moving load on a layered half plane. J. Eng. Mech. Div. ASCE 87(EM4), 75–89 (1961)
Miles, I.W.: Response of a layered half-space to a moving load. J. Appl. Mech. 33, 680–681 (1966)
Achenbach, J.D., Keshava, M.S.P., Hermann, G.: Moving loads on a plate resting on an elastic half-space. J. Appl. Mech. 34, 910–914 (1967)
Chonan, S.: Moving load on a pre-stressed plate resting on a fluid half-space. Arch. Appl. Mech. 45, 171–178 (1976)
Ungar, A.: Wave generation in an elastic half-space by a normal point load moving uniformly over the free surface. Int. J. Eng. Sci. 14, 935–945 (1976)
Olsson, M.: On the fundamental moving load problem. J. Sound Vib. 145, 299–307 (1991)
Lee, H.P., Ng, T.Y.: Dynamic response of a cracked beam subject to a moving load. Acta Mech. 106, 221–230 (1994)
Alekseyeva, L.A.: The dynamics of an elastic half-space under the action of a moving load. J. Appl. Math. Mech. 71, 511–518 (2007)
Chattopadhyay, A., Saha, S.: Dynamic response of normal moving load in the plane of symmetry of a monoclinic half space. Tamkang J. Sci. Eng. 9(4), 307–312 (2006)
Chattopadhyay, A., Sahu, S.A.: Stresses produced in slightly compressible, finitely deformed elastic media due to a normal moving load. Arch. Appl. Mech. 82, 699–708 (2012)
Chattopadhyay, A., Gupta, S., Sharma, V.K., Kumari, P.: Stresses produced on a rough irregular half-space by a moving load. Acta Mech. 221, 271–280 (2011)
Chatterjee, M., Dhua, S., Chattopadhyay, A.: Response of moving load due to irregularity in slightly compressible, finitely deformed elastic media. Mech. Res. Commun. 66, 49–59 (2015)
Chatterjee, M., Dhua, S., Sahu, S.A., Chattopadhyay, A.: Reflection in a highly anisotropic medium for three-dimensional plane waves under initial stresses. Int. J. Eng. Sci. 85, 136–149 (2014)
Chatterjee, M., Dhua, S., Chattopadhyay, A.: Quasi-P and quasi-S waves in a self-reinforced medium under initial stresses and under gravity. J. Vib. Control (2015). doi:10.1177/1077546314568694
Chatterjee, M., Dhua, S., Chattopadhyay, A., Sahu, S.A.: Seismic waves in heterogeneous crust-mantle layers under initial stresses. J. Earthq. Eng. (2015). doi:10.1080/13632469.2015.1038371
Chatterjee, M., Dhua, S., Chattopadhyay, A., Sahu, S.A.: Reflection and refraction for three-dimensional plane waves at the interface between distinct anisotropic half spaces under initial stresses. Int. J. Geomech. (2015). doi:10.1061/(ASCE)GM.1943-5622.0000601
Sato, Y.: Study on surface waves. VI: Generation of Love and other types of SH waves. Bull. Earthq. Res. Inst. 30, 101 (1952)
Denoyer, J.: The effect of variations in layer thickness of Love waves. Bull. Seismol. Soc. Am. 51(2), 227–235 (1961)
Chattopadhyay, A.: On the dispersion equations for Love waves due to irregularity in the thickness of non-homogeneous crustal layer. Acta Geophys. Pol. 23, 307–317 (1975)
Mukhopadhyay, A.: Stresses produced by a normal load moving over a transversely isotropic layer of ice lying on a rigid foundation. Pure Appl. Geophys. 60(1), 29–41 (1965)
Chung, H., Linton, C.: Reflection and transmission of waves across a gap between two semi-infinite elastic plates on water. Q. J. Mech. Appl. Math. 58(1), 1–15 (2005)
Hearmon, R.F.S.: An Introduction to Applied Anisotropic Elasticity. Oxford University Press, London (1961)
Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Oxford University Press, London (1952)
Ewing, W.M., Jardetzky, W.S., Press, F.: Elastic Waves in Layered Media. McGraw Hill, New York (1957)
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Chatterjee, M., Chattopadhyay, A. Effect of moving load due to irregularity in ice sheet floating on water. Acta Mech 228, 1749–1765 (2017). https://doi.org/10.1007/s00707-016-1786-z
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DOI: https://doi.org/10.1007/s00707-016-1786-z