Coupled pairs of dual integral equations with trigonometric kernels
Authors:
R. Khadem and L. M. Keer
Journal:
Quart. Appl. Math. 31 (1974), 467-480
MSC:
Primary 45F10
DOI:
https://doi.org/10.1090/qam/448002
MathSciNet review:
448002
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Abstract: The solution is given to a system of two pairs of dual integral equations with constant coefficients involving trigonometric kernels. The method is analogous to that applied to Bessel function kernels and involves reduction to a single Wiener—Hopf equation for which a solution is available. The example of an indenter moving with friction present is worked out by this method and also by means of equivalent reduction of the system of equations to a singular integral equation.
- R. Khadem, On two pairs of simultaneous dual integral equations, J. Engrg. Math. 5 (1971), 121–126. MR 367582, DOI https://doi.org/10.1007/BF01535403
- D. A. Spence, A Wiener-Hopf equation arising in elastic contact problems, Proc. Roy. Soc. London Ser. A 305 (1968), 81–92. MR 226906, DOI https://doi.org/10.1098/rspa.1968.0106
J. W. Craggs and A. M. Roberts, On the motion of a heavy cylinder over the surface on an elastic solid J. Appl. Mech. 34, 207–209 (1967)
A. M. Roberts, A two-dimensional mixed boundary-values problem in elasticity, Quart. Appl. Math. 28, 445–449 (1970)
A. M. Roberts, Further two-dimensional effects of cylinders rolling on an elastic half-space, Quart. Appl. Math. 29, 17–28 (1971)
J. Brilla, Contact problems of an elastic anisotropic half-plane, Revue Mech. Appl. Buc. 7, 617–642 (1962)
J. B. Alblas and M. Kuipers, Contact problems of a rectangular block on an elastic layer of finite thickness, Acta Mech. 9, 1–12 (1970)
J. B. Alblas and M. Kuipers, On the two-dimensional problem of a cylindrical stamp pressed into a thin elastic layer, Acta Mech. 9, 292–311 (1970)
J. B. Alblas and M. Kuipers, The two-dimensional contact problem of a rough stamp sliding slowly on an elastic layer—general considerations and thick layer asymptotes, Int. J. Solids Structures 7, 99–109 (1971)
J. B. Alblas and M. Kuipers, The Two-dimensional contact problem of a rough stamp sliding slowly on an elastic layer—II. Thin layer asymptotes, Int. J. Solids Structures 7, 225–237 (1971)
L. M. Keer and J. M. Freedman, Static response of a rigid strip bonded to an elastic layer, Acta Mechanica, 17, 1–15 (1973)
E. C. Titchmarsh, Theory of Fourier integrals, Oxford at the Clarendon Press, 1962, p. 25
N. I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, Noordhoff, Holland, p. 498
- M. J. Lighthill, Introduction to Fourier analysis and generalised functions, Cambridge University Press, New York, 1960. MR 0115085
- D. A. Spence, Self similar solutions to adhesive contact problems with incremental loading, Proc. Roy. Soc. London Ser. A 305 (1968), 55–80. MR 226905, DOI https://doi.org/10.1098/rspa.1968.0105
L. M. Keer, Mixed boundary value-problems for an elastic half-space, Proc. Camb. Phil. Soc. 63, 1379–1386 (1967)
R. Khadem, On two pairs of simultaneous dual integral equations, J. Eng. Math. 5, 121–126 (1971)
D. A. Spence, Wiener-Hopf equation arising in elastic contact problems, Proc. Roy. Soc. London A 305, 81–92 (1968)
J. W. Craggs and A. M. Roberts, On the motion of a heavy cylinder over the surface on an elastic solid J. Appl. Mech. 34, 207–209 (1967)
A. M. Roberts, A two-dimensional mixed boundary-values problem in elasticity, Quart. Appl. Math. 28, 445–449 (1970)
A. M. Roberts, Further two-dimensional effects of cylinders rolling on an elastic half-space, Quart. Appl. Math. 29, 17–28 (1971)
J. Brilla, Contact problems of an elastic anisotropic half-plane, Revue Mech. Appl. Buc. 7, 617–642 (1962)
J. B. Alblas and M. Kuipers, Contact problems of a rectangular block on an elastic layer of finite thickness, Acta Mech. 9, 1–12 (1970)
J. B. Alblas and M. Kuipers, On the two-dimensional problem of a cylindrical stamp pressed into a thin elastic layer, Acta Mech. 9, 292–311 (1970)
J. B. Alblas and M. Kuipers, The two-dimensional contact problem of a rough stamp sliding slowly on an elastic layer—general considerations and thick layer asymptotes, Int. J. Solids Structures 7, 99–109 (1971)
J. B. Alblas and M. Kuipers, The Two-dimensional contact problem of a rough stamp sliding slowly on an elastic layer—II. Thin layer asymptotes, Int. J. Solids Structures 7, 225–237 (1971)
L. M. Keer and J. M. Freedman, Static response of a rigid strip bonded to an elastic layer, Acta Mechanica, 17, 1–15 (1973)
E. C. Titchmarsh, Theory of Fourier integrals, Oxford at the Clarendon Press, 1962, p. 25
N. I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, Noordhoff, Holland, p. 498
M. J. Lighthill, Introduction to Fourier analysis and generalized functions, Cambridge University Press, 1959, p. 15
D. A. Spence, Self-similar solutions to adhesive contact problems with incremental loading, Proc. Roy. Soc. London A 305, 5–80, (1968)
L. M. Keer, Mixed boundary value-problems for an elastic half-space, Proc. Camb. Phil. Soc. 63, 1379–1386 (1967)
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Article copyright:
© Copyright 1974
American Mathematical Society
