The Imbedding Method in Statistical Boundary-Value Wave Problems

1994 ◽  
pp. 1-127 ◽  
Author(s):  
V.I. Klyatskin
Keyword(s):  
Boundary Value ◽  
Statistical Boundary ◽  
Imbedding Method ◽  
Wave Problems

scholarly journals Расчет нормальных температурных напряжений в компонентах асфальтобетона методами статистической механики композитов

2020 ◽  
Vol 44 (3) ◽  
pp. 13-21
Author(s):  
Keyword(s):  
Boundary Value Problem ◽  
Asphalt Concrete ◽  
Thermal Stresses ◽  
Boundary Value ◽  
Temperature Stresses ◽  
Surface Strength ◽  
Experimental Modelling ◽  
Statistical Boundary ◽  
Mechanics Of Composites ◽  
Distribution Of Components

Учет температурных напряжений важен при выполнении расчетов на прочность дорожного покрытия. В данной статье приводятся результаты исследования распределения нормальных температурных напряжений для компонент асфальтобетона. Показано логарифмически нормальное распределение нормальных температурных напряжений для включения и распределение Гаусса для нормальных температурных напряжений связующего. Исследование проведено с применением теоретических методов статистической механики композитов, аналитических методов решения статистической краевой задачи механики композитов, математического моделирования, методов программирования в математическом пакете MathCad. Ключевые слова: асфальтобетон, температурные напряжения, статистическая краевая задача механики композитов, математическое моделирование, пакет программ. Consideration of temperature stresses is important when performing calculations of road surface strength. The results of study of the distribution of temperature stresses components for asphalt concrete are given herein. Lognormal distribution of components of thermal stresses for inclusion and normal distribution of components for thermal stresses of thebinding agent are shown. The study was carried out using theoretical methods of mechanics of composites, analytical methods for solving the statistical boundary value problem of mechanics of composites, numerical and experimental modelling, programming methods in the mathematical package MathCad. Keywords: asphalt concrete, temperature stresses, statistical boundary value problem, mechanics of composites, numerical experiment, laboratory experiment.

A Nystrom method for a boundary value problem arising in unsteady water wave problems

2010 ◽  
Vol 31 (3) ◽  
pp. 1123-1153
Author(s):  
M. D. Preston ◽  
P. G. Chamberlain ◽  
S. N. Chandler-Wilde
Keyword(s):  
Boundary Value Problem ◽  
Water Wave ◽  
Boundary Value ◽  
Nyström Method ◽  
Nystrom Method ◽  
Wave Problems

scholarly journals Generalized Form of the Invariant Imbedding Method and Its Application to the Study of Back-Scattering in Shallow-Water Acoustics

2021 ◽  
Vol 9 (9) ◽  
pp. 1033
Author(s):  
Mikhail Kazak ◽  
Konstantin Koshel ◽  
Pavel Petrov
Keyword(s):  
Shallow Water ◽  
Acoustic Waves ◽  
Boundary Value ◽  
Coupled Systems ◽  
Problem Solution ◽  
Invariant Imbedding ◽  
Coupled Equations ◽  
Back Scattering ◽  
Invariant Imbedding Method ◽  
Imbedding Method

A generalized form of the matrix-invariant imbedding method was developed to solve boundary-value problems for coupled systems of Helmholtz-type equations. Within this approach, a boundary-value problem solution can be obtained by solving evolutionary first-order imbedding equations for a matrix-valued function. The proposed method is applied to the solution of coupled equations for mode amplitudes describing the propagation of acoustic waves in a range-dependent shallow-water waveguide. The back-scattering of modes by bathymetry features is investigated, and the coefficients of the modal expansion of the wave reflected by an inhomogeneity in the bottom relief are computed. It is demonstrated that back-scattering is strongly connected with the modal interactions and that the back-scattered field consists of modes with numbers different from the number of the incident mode.

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