Abstract
A boundary-value problem for a three-dimensional Helmholtz equation in a domain shaped as an unbounded rectangular wedge is under consideration. An exact solution to this boundary-value problem is constructed in the form of a packed block element necessary for investigating more complex and even mixed problems for block structures. Packed blocks are joined into a block structure by creating quotient topologies of the topological spaces of blocks, and the equivalence relations are interblock boundary conditions.
Similar content being viewed by others
References
L. M. Brekhovskikh, Waves in Layered Media (Nauka, Moscow, 1973; Academic Press, 1960).
V. M. Babich, “On the Short-Wave Asymptotic Behaviour of the Green’s Function for the Helmholtz Equation,” Mat. Sb. 65(107) (4), 576–630 (1964).
V. M. Babich, and V. S. Buldyrev, Asymptotic Methods in Short-Wavelength Diffraction Theory (Nauka, Moscow, 1972; Alpha Sci. International Ltd, 2009).
I. V. Mukhina, “Approximate Reduction of the Equations of the Theory of Elasticity and Electrodynamics for Inhomogeneous Media to the Helmholtz Equations,” Prikl. Mat. Mekh. 36 (4), 667–671 (1972).
L. A. Molotkov, Wave Propagation in Porous and Cracked Media, Studied on the Basis of Effective Biot Models and Layered Media (Nauka, St. Petersburg, 2001) [in Russian].
W. Nowacki, Teoria Sprezystosci (Panstwowe Wydawnictwo Naukowe, Warsaw, 1970).
W. Nowacki, Efekty Elektromagnetyczne W Stalych Cialach Odksztalcalnych (Panstwowe Wydawnictwo Naukowe, Warsaw, 1983).
L. A. Tkacheva, “Vibrations of a Floating Elastic Plate Due to Periodic Displacements of a Bottom Segment,” Prikl. Mekh. Tekh. Fiz. 46 (5), 166–179 (2005) [J. Appl. Mech. Tech. Phys. 46 (5), 754–765 (2005)].
L. A. Tkacheva “Plane Problem of Vibrations of an Elastic Floating Plate under Periodic External Loading,” Prikl. Mekh. Tekh. Fiz. 45 (3), 136–145 (2004) [J. Appl. Mech. Tech. Phys. 45 (3), 420–427 (2004)].
L. A. Tkacheva “Behavior of a Floating Elastic Plate during Vibrations of a Bottom Segment,” Prikl. Mekh. Tekh. Fiz. 46 (2), 98–108 (2005) [J. Appl. Mech. Tech. Phys. 46 (2), 230–238 (2005)].
L. A. Tkacheva “Interaction of Surface and Flexural-Gravity Waves in Ice Cover with a Vertical Wall,” Prikl. Mekh. Tekh. Fiz. 54 (4), 158–170 (2013) [J. Appl. Mech. Tech. Phys. 54 (4), 651–661 (2013)].
V. A. Babeshko, O. V. Evdokimova, O. M. Babeshko, and I. V. Ryadchikov, “Method for Designing Inhomoge-neous Materials and Structures,” Dokl. Akad. Nauk 482 (4), 398–402 (2018); DOI: 10.1134/S1028335818100014.
V. A. Babeshko, O. V. Edvokimova, and O. M. Babeshko, “Stages of Block Element Transformation,” Dokl. Akad. Nauk 468 (2), 154–158 (2016).
V. A. Babeshko, O. M. Babeshko, and O. V. Evdokimova, “Savovskii Problem of Block Structures,” Dokl. Akad. Nauk 427 (4), 480–485 (2009).
M. V. Fedoryuk, The Pass Method (Nauka, Moscow, 1977) [in Russian].
M. V. Fedoryuk, The Pass Method (Nauka, Moscow, 1977) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.A. Babeshko, O.V. Evdokimova, O.M. Babeshko.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 60, No. 6, pp. 90–96, November-December, 2019. Original article submitted June 7, 2019
Rights and permissions
About this article
Cite this article
Babeshko, V.A., Evdokimova, O.V. & Babeshko, O.M. Problem of Studying the Acoustic and Hydrodynamic Properties of the Medium that Occupies a Domain Shaped As a Three-Dimensional Rectangular Wedge. J Appl Mech Tech Phy 60, 1054–1059 (2019). https://doi.org/10.1134/S0021894419060105
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894419060105