Interaction of water waves with thin plates

Various problems involving the interaction of water waves with thin plates are reduced to hypersingular boundary integral equations. Examples include scattering by submerged curved plates and by surface-piercing plates, in two dimensions; trapping of waves by submerged plates; and scattering by submerged at plates in three dimensions. Each integral equation is solved numerically,

[1]  Paul A. Martin,et al.  Mapping flat cracks onto penny-shaped cracks, with application to somewhat circular tensile cracks , 1996 .

[2]  F. Rizzo,et al.  HYPERSINGULAR INTEGRALS: HOW SMOOTH MUST THE DENSITY BE? , 1996 .

[3]  Paul A. Martin,et al.  Trapping of water waves by submerged plates using hypersingular integral equations , 1995, Journal of Fluid Mechanics.

[4]  P. A. Martin.  Mapping flat cracks onto penny-shaped cracks: Shear loadings , 1995 .

[5]  Paul A. Martin,et al.  Scattering of water waves by submerged curved plates and by surface-piercing flat plates , 1994 .

[6]  Allen T. Chwang,et al.  Analysis of Wave Scattering by Submerged Circular Disk , 1993 .

[7]  V. Ervin,et al.  Collocation with Chebyshev polynomials for a hypersingular integral equation on an interval , 1992 .

[8]  F. J. Rizzo,et al.  Continuity requirements for density functions in the boundary integral equation method , 1992 .

[9]  J. Dewynne,et al.  Calculation of the opening displacement of surface-breaking plane cracks , 1992 .

[10]  Paul A. Martin,et al.  Exact Solution of a Simple Hypersingular Integral Equation , 1992 .

[11]  Paul A. Martin,et al.  Scattering of water waves by submerged plates using hypersingular integral equations , 1992 .

[12]  D. Evans,et al.  TRAPPED MODES ABOVE A SUBMERGED HORIZONTAL PLATE , 1991 .

[13]  A note on waves due to rolling of a partially immersed nearly vertical plate , 1991 .

[14]  Paul A. Martin,et al.  End-point behaviour of solutions to hypersingular integral equations , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[15]  L. Schmerr,et al.  Hypersingular Boundary Integral Equations: Some Applications in Acoustic and Elastic Wave Scattering , 1990 .

[16]  Frank J. Rizzo,et al.  On boundary integral equations for crack problems , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[17]  A. Chakrabarti,et al.  A Note on Diffraction of Water Waves by a Nearly Vertical Barrier , 1989 .

[18]  Seyed Mehdi Sobhani,et al.  Interaction of Periodic Waves with Inclined Portable Barrier , 1988 .

[19]  M. Golberg.  The convergence of several algorithms for solving integral equations with finite part integrals. II , 1987 .

[20]  J. Miles.  On surface-wave forcing by a circular disk , 1987, Journal of Fluid Mechanics.

[21]  Begnaud Francis Hildebrand,et al.  Introduction to numerical analysis: 2nd edition , 1987 .

[22]  Paul A. Martin.  ORTHOGONAL POLYNOMIAL SOLUTIONS FOR PRESSURIZED ELLIPTICAL CRACKS , 1986 .

[23]  M. Gutknecht.  Numerical conformal mapping methods based on function conjugation , 1986 .

[24]  A. Kaya,et al.  On the solution of integral equations with strongly singular kernels , 1985 .

[25]  M. Mciver.  Diffraction of water waves by a moored, horizontal, flat plate , 1985 .

[26]  P. A. Martin.  On the T-matrix for water-wave scattering problems , 1985 .

[27]  D. Evans,et al.  The trapping of surface waves above a submerged, horizontal cylinder , 1985, Journal of Fluid Mechanics.

[28]  D. C. Shaw.  Perturbational Results for Diffraction of Water-waves by Nearly-vertical Barriers , 1985 .

[29]  Mana Patarapanich,et al.  Forces and moment on a horizontal plate due to wave scattering , 1984 .

[30]  A Chebyshev expansion of singular integrodifferential equations with a ∂2 In |s − t|/∂s ∂t kernel , 1983 .

[31]  P. Liu,et al.  Wave Scattering by a Rigid Thin Barrier , 1982 .

[32]  Paul A. Martin,et al.  The discontinuity in the elastostatic displacement vector across a penny-shaped crack under arbitrary loads , 1982 .

[33]  Steen Krenk,et al.  A Circular Crack Under Asymmetric Loads and Some Related Integral Equations , 1979 .

[34]  Kendall E. Atkinson.  An introduction to numerical analysis , 1978 .

[35]  R. W. Lardner,et al.  Penny-shaped cracks , 1975 .

[36]  Chris Garrett,et al.  Wave forces on a circular dock , 1971, Journal of Fluid Mechanics.

[37]  J. Miles.  A note on variational principles for surface-wave scattering , 1971, Journal of Fluid Mechanics.

[38]  D. V. Evans,et al.  Diffraction of water waves by a submerged vertical plate , 1970, Journal of Fluid Mechanics.

[39]  John W. Miles,et al.  Scattering of gravity waves by a circular dock , 1968, Journal of Fluid Mechanics.

[40]  J. E. Burke,et al.  Scattering of Surface Waves on an Infinitely Deep Fluid , 1964 .

[41]  V. Smirnov,et al.  A course of higher mathematics , 1964 .

[42]  W. D. Kim.  The pitching motion of a circular disk , 1963, Journal of Fluid Mechanics.

[43]  F. Ursell,et al.  Surface waves generated by an oscillating circular cylinder on water of finite depth: theory and experiment , 1961, Journal of Fluid Mechanics.

[44]  R. MacCamy.  On the heaving motion of cylinders of shallow draft , 1961 .

[45]  R. MacCamy.  On the scattering of water waves by a circular disk , 1961 .

[46]  H. Kober,et al.  Dictionary of conformal representations , 1957 .

[47]  T. MacRobert.  Higher Transcendental Functions , 1955, Nature.

[48]  F. Ursell,et al.  Trapping modes in the theory of surface waves , 1951, Mathematical Proceedings of the Cambridge Philosophical Society.

[49]  W. S. Hamilton.  Forces exerted by waves on a sloping board , 1950 .

[50]  W. R. Dean,et al.  Surface waves on deep water in the presence of a submerged circular cylinder. I , 1950, Mathematical Proceedings of the Cambridge Philosophical Society.

[51]  W. R. Dean.  On the reflexion of surface waves by a submerged circular cylinder , 1948, Mathematical Proceedings of the Cambridge Philosophical Society.

[52]  W. R. Dean,et al.  The effect of a fixed vertical barrier on surface waves in deep water , 1947, Mathematical Proceedings of the Cambridge Philosophical Society.

[53]  T. Havelock,et al.  LIX.Forced surface-waves on water , 1929 .