Conclusion
The results presented in here permit us to construct approximate solutions of problems of steady-state diffraction of waves of different physical nature at finite bodies of revolution. In each approximation the problems reduce to the problems of diffraction in a spherical system of coordinates with the right sides of the boundary conditions changing in each approximation and with identical homogeneous wave equations in all the approximations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature Cited
G. Beitmen, Mathematical Theory of Propagation of Electromagnetic Waves [in Russian], Fizmatgiz, Moscow (1958).
D. Bland, Theory of Linear Viscoelasticity, Pergamon, New York (1960).
G. N. Watson, Theory of Bessel Functions, Camb. U. P., New York.
E. W. Hobson, Theory of Spherical and Ellipsoidal Functions [Russian translation], IL, Moscow (1952).
L. D. Goldshtein and N. V. Zerov, Electromagnetic Fields and Waves [in Russian], Sovetskoe Radio, Moscow (1956).
O. M. Guz', Prikl. Mekhan.,8, No. 6 (1962).
O. M. Guz', Dokl. Akad. Nauk UkrSSR, Ser. A, No. 4 (1970).
A. N. Guz', I. S. Chernyshenko, and K. I. Shnerenko, Spherical Bottom Weakened by Holes [in Russian], Naukova Dumka, Kiev (1970).
O. M. Guz' and M. O. Shul'ga, Dokl. Akad. Nauk UkrSSR, Ser. A, No. 11 (1970).
A. N. Guz' and V. I. Golovchan, Diffraction of Elastic Waves in Multiply Connected Bodies [in Russian], Naukova Dumka, Kiev (1972).
Diffraction of Electromagnetic Waves at Some Bodies of Revolution, Sovetskoe Radio, Moscow (1957).
E. A. Ivanov, Diffraction of Electromagnetic Waves at Two Bodies [in Russian], Nauka i Tekhnika, Minsk (1968).
L. D. Landau and E. M. Lifshits, Theory of Fields [in Russian], Fizmatgiz, Moscow (1962).
J. W. Miles, Potential Theory of Nonsteady Super Sonic Flows [translated from English], Fizmatgiz, Moscow (1963).
R. von Mises, Mathematical Theory of Compressible Fluid Flow, Acad. Pr., New York (1958).
P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. 1, McGraw-Hill, New York (1953).
Yu. N. Nemish, Approximate Solutions of Spatial Problems of the Theory of Elasticity for Transversally Isotropic Medium, Prikl. Mekhan.,5, No. 8 (1969).
Yu. M. Nemish, Dokl. Akad. Nauk UkrSSR, Ser. A, No. 11 (1970).
Yu. N. Nemish, Stressed State of Nonlinear-Elastic Bodies, Izv. AN SSSR, Mekhan. Tverdogo Tela, No. 4 (1971).
Yu. N. Nemish, V. N. Nemish, and P. F. Yarema, Distribution of Stresses around Noncanonical Surfaces, Prikl. Mekhan.,7, No. 12 (1971).
J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York (1941).
M. O. Shul'ga, Dokl. Akad. Nauk UkrSSR, Ser. A, No. 10 (1968).
C. Flammer, Spheroidal Wave Functions, Stanford Univ. Press (1957).
S. Meixner and F. M. Schafke, Mathieu Functions and Spheroidal Functions, Springer-Verlag, Berlin (1954).
G. N. Sawin, A. N. Guz', and A. S. Kosmodamianski, Mechanika teoretyczna i stosowana,8, No. 1 (1970).
Additional information
Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 9, No. 7, pp. 10–18, July, 1973.
Rights and permissions
About this article
Cite this article
Guz', A.N. Diffraction of waves at finite bodies of revolution. Soviet Applied Mechanics 9, 704–710 (1973). https://doi.org/10.1007/BF00882992
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00882992