AN ANALYTICAL SOLUTION OF SECOND-ORDER WAVE FORCEON A VERTICAL CIRCULAR CYLINDER

摘要/Abstract

摘要： So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.

关键词: plastic deformation, incremental collapse, kinematicalshakedown theorem, water wave, second-order force, radiation condition, diffraction

Abstract: So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.

Key words: plastic deformation, incremental collapse, kinematicalshakedown theorem, second-order force, radiation condition, diffraction, water wave

邹志利;戴遗山. AN ANALYTICAL SOLUTION OF SECOND-ORDER WAVE FORCEON A VERTICAL CIRCULAR CYLINDER[J]. Applied Mathematics and Mechanics (English Edition), 1994, 15(9): 849-863.

Zhou Zhi-li;Dai Yi-shan. AN ANALYTICAL SOLUTION OF SECOND-ORDER WAVE FORCEON A VERTICAL CIRCULAR CYLINDER[J]. Applied Mathematics and Mechanics (English Edition), 1994, 15(9): 849-863.

参考文献

[1] Yamaguchi, M.and Y.Tsuchiya, Nonlinear effect of waves on wave pressure and wave force on a large cylindrical pile, Proceeding of Civil Engineering Society in Japan, No. 229, Sep., (1974). (in Japanese).
[2] Raman, H., N. Jothishankar and P. Vendatanarasaiah, Nonlinear wave interaction with vertical cylinder of large diameter, J. of Ship Research, 21, 2, June(1977).
[3] Chakrabarti, S. K., Comments on second-order wave effects on large-diameter vertical cylinder, J. of Ship Research, 22, 4, Dec., (1978).
[4] Molin, B., Second order diffraction loads upon three-dimensional bodies, Appl. Ocean Re., 1, 4, (1979).
[5] Hunt, J. N. and R. E. Baddour, Second-order wave forces on vertical cylinder, J. of the Waterway, Port, Coastal and Ocean Division, ASCE. 108, WW3, Aug., (1982).
[6] Chen, M. and R. T. Hudspeth, Nonlinear diffraction by eigenfunction expansions, J. of the Waterit}av, Port, Coastal and Oceun Diai.sion, ASCE, 108, Aug., (1982).
[7] Chakrabati, S. K., Nonlinear wave effect on large offshore structure, Second International Symposium on Ocean Engineering and Ship Handling, (1983).
[8] He Wu-zhou and Dai Yi-sham On the calculation of three-dimensional hydodynamic coefficients by simple Greer's functSon technique, Shipbuilding of Clrina, 2.(1986). (in Chinese).
[9] Zhou Chin-pu, On the radiation condition of nonlinear wave scattering problem for a vertical cylinder, ACTH Mechunica Sinica, 17, 1, ( 1985). (in Chinese).
[10] Miao Guo-ping and Liu Ying-zhong, Second order wave forces on large-diameter vertical circular cylinders, Shipbuilding of Chirtu, 3, (1987). (in Chinese).
[11] Kim, M. H. and D. K. P. Yue, The complete second-order diffraction solution for an axisymmetric body, J. of Fluid Meclt., 200, (1989).
[12] Zhou, Zhi-li, The second-order diffraction problem of a three-dimensional bady subjected to stokes wave, Ph, D. Thesis, Harbin Shipbuilding Engineering Institute, (1989). (in Chinese).
[13] Mei C. C. Water Wave Hydrodynamics, Science Press, Beijing, China, (1984). (in Chinese).
[14] Abramowitz, M. and 1. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Washington, D. C., (1964).

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