Abstract
Problems of nonstationary scattering of incident waves by unclosed surfaces have been solved in the general formulation under the usual assumptions of the linear mechanics of ideal compressible fluids. Such problems are encountered in a number of important hydrodynanic applications. In this case the nonstationary wave field must be known at any distance from the scatterer, and in particular in its immediate vicinity. The known methods of stationary diffraction cannot be used in nonstationary problems, when it is not possible to obtain exact expressions for the Fourier transforms of the unknown solutions and hence guarantee the unique recovery of the inverse transforms. However, the direct solution of the nonstationary problem is possible only in very simple situations: scattering of pressure waves by a plate, diffraction at the edge of a half-plane or at a slit in a flat screen, etc. These circumstances make it necessary to develop special approaches to the solution of the problem of the nonstationary scattering of pressure waves in a fluid by arbitrary unclosed surfaces. This paper outlines a method which leads to the construction of the Laplace transforms of the unknown solutions and is based on a unique means of satisfying the boundary conditions with the subsequent obtaining of exact expressions for the coefficients (densities) of the expansions employed. The class of problems solvable by this method is confined to those for which it is possible to obtain corresponding solutions by expansion in series or integrals over the complete orthogonal system of eigenfunctions on the assumption that the surface of the obstacle is closed. The Laplace transforms of the solutions can be inverted by any approximate method. The solutions constructed in accordance with the formalism developed are in satisfactory agreement with the experimental data and coincide with the classical results.
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A. G. Gorshkov, “Interaction of shock waves and deformable barriers,” in: Advances in Science and Technology (All-Union Institute of Scientific and Technical Information). Mechanics of Deformable Bodies, Vol. 13 [in Russian], Moscow (1980), pp. 105–136.
H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung, in: Handbuch der Physik (ed. by S. Flugge), Vol. 25, Part l, Springer Verlag, Berlin (1961), pp. 218–573.
V. V. Dykhta, Method of Integral Transforms in Wave Problems of Hydroacoustics [in Russian], Naukova Dumka, Kiev (1981).
V. P. Shestopalov, Summator Equations in Modern Diffraction Theory [in Russian], Naukova Dumka, Kiev (1983).
V. V. Dykhta, “A method of solving problems of nonstationary diffraction of acoustic waves by thin unclosed shells,” Dokl. Akad. Nauk Uzb. SSR, Ser. A, No. 1, 43 (1983).
V. P. Shestopalov, Method of the Riemann-Hilbert Problem in the Theory of Diffraction and Propagation of a Electromagnetic Waves [in Russian], Izd. Khar'k. Univ., Khar'kov (1971).
E. V. Krivitskii and V. V. Shamko, Transient Processes Associated with a High-Voltage Discharge in Water [in Russian], Naukova Dumka, Kiev (1979).
A. Erdélyi (ed.), Tables of Integral Transforms, Vol. 1, California Institute of Technology Bateman MS Project, New York (1954).
F. G. Friedlander, Sound Pulses [Russian translation], Izd. Inostr. Lit., Moscow (1962).
V. I. Krylov and N. S. Skoblya, Approximate Fourier Transformation and Laplace Transform Inversion Methods [in Russian], Nauka, Moscow (1974).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 84–91, November–December, 1985.
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Dykhta, V.V. Theory of nonstationary interaction between pressure waves in a fluid and unclosed surfaces. Fluid Dyn 20, 906–912 (1985). https://doi.org/10.1007/BF01049934
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DOI: https://doi.org/10.1007/BF01049934