scholarly journals On Peculiarities of Propagation of a Plane Elastic Wave through a Gradient Anisotropic Layer

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Anastasiia Anufrieva ◽  
Dmitry Chickrin ◽  
Dmitrii Tumakov
Keyword(s):  
Boundary Value Problem ◽  
Elastic Wave ◽  
Longitudinal Wave ◽  
Energy Flow ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Normal Component ◽  
Grid Method ◽  
Anisotropic Layer ◽  
Plane Longitudinal Wave

The problem of diffraction of a plane elastic wave by an anisotropic layer is studied. The diffraction problem is reduced to a boundary value problem for the layer. The grid method is used for solving the resulting boundary value problem. The diffraction of a plane longitudinal wave by the layer is considered. Some peculiarities of the gain-frequency and the gain-angle characteristics of a normal component of an energy flow of a passed longitudinal wave are numerically studied.

scholarly journals Inverse boundary-value problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5259-5271
Author(s):  
Elvin Azizbayov ◽  
Yashar Mehraliyev
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Longitudinal Wave ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Boundary Value ◽  
Inverse Boundary ◽  
Longitudinal Wave Propagation

We study the inverse coefficient problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions. The main purpose of this paper is to prove the existence and uniqueness of the classical solutions of an inverse boundary-value problem. To investigate the solvability of the inverse problem, we carried out a transformation from the original problem to some equivalent auxiliary problem with trivial boundary conditions. Applying the Fourier method and contraction mappings principle, the solvability of the appropriate auxiliary inverse problem is proved. Furthermore, using the equivalency, the existence and uniqueness of the classical solution of the original problem are shown.

The Diffraction Forces for a Ship Moving in Oblique Seas

1979 ◽  
Vol 23 (02) ◽  
pp. 127-139
Author(s):  
Armin Walter Troesch
Keyword(s):  
Boundary Value Problem ◽  
Surface Condition ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Second Order ◽  
Exciting Force ◽  
Forward Speed ◽  
Order Problem ◽  
Incident Waves ◽  
The Waves

The diffraction problem of a fixed slender ship moving in incident waves is formulated. The waves are assumed to be of the same order as the beam of the ship and are from an oblique heading. The boundary value problem is linearized with respect to wave amplitude and solved by the method of matched asymptotic expansions. The oscillating forward-speed potential is solved to two orders of magnitude. The first order is just the zero-speed case while the second-order problem involves solving a boundary-value problem with a nonhomogeneous free-surface condition. The solution to this second-order problem is given in terms of three auxiliary potentials, each satisfying a separate part of the boundary conditions. For zero forward speed, the sectional exciting force is calculated and compared with the commonly used integrand of the Khaskind relations. The two give different values, but when integrated over the hull both show the same total exciting force. The pressure distribution on an ore carrier for both zero forward speed and an abbreviated form of the forward-speed case is given and compared with experiments.

On the Computation of Wave Induced Bending and Torsion Moments

1971 ◽  
Vol 15 (03) ◽  
pp. 217-220
Author(s):  
T. Francis Ogilvie
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Vertical Plane ◽  
Bending Moment ◽  
Ship Motions ◽  
Wave Loads ◽  
Cross Member ◽  
Wave Induced ◽  
Incident Waves

In the calculation of wave loads on a ship, one must consider the effects of both the incident waves and the diffraction waves (the latter being caused by the presence of the ship in the incident waves). In the ship-motions problem, Khaskind showed how one can do this without having to solve the diffraction-wave boundary-value problem. Khaskind's procedure is here extended to the calculation of structural loads on a ship. Two examples are discussed: (i) bending moment in the vertical plane of a ship in waves and (ii) torsion in the cross member of a catamaran. Many other applications are possible. In each case, it is necessary to solve a boundary-value problem, but it is generally much simpler than the diffraction problem.

Weighted Estimates for Boundary Value Problems with Fractional Derivatives

2020 ◽  
Vol 20 (4) ◽  
pp. 609-630 ◽  
Author(s):  
Ivan P. Gavrilyuk ◽  
Volodymyr L. Makarov ◽  
Nataliya V. Mayko
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Fractional Derivatives ◽  
Dirichlet Boundary ◽  
Boundary Effect ◽  
Boundary Value ◽  
Grid Method ◽  
Weighted Estimates ◽  
Regularity Properties ◽  
Better Than

AbstractWe consider the Dirichlet boundary value problem for linear fractional differential equations with the Riemann–Liouville fractional derivatives. By transforming the boundary value problem to the integral equation, some regularity properties of the exact solution are derived. Based on these properties, the numerical solution of the boundary value problems by a grid method is discussed and weighted estimates considering the boundary effect are obtained. It is shown that the accuracy (the convergence rate) near the boundary is better than inside the domain due to the influence of the Dirichlet boundary condition.

scholarly journals The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces

2006 ◽  
Vol 13 (2) ◽  
pp. 251-260
Author(s):  
Luis P. Castro ◽  
David Natroshvili
Keyword(s):  
Boundary Value Problem ◽  
Wave Diffraction ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Potential Method ◽  
Wave Number ◽  
Dimensional Case ◽  
Bessel Potential ◽  
Regularity Properties ◽  
Bessel Potential Spaces

Abstract This paper is concerned with a screen type boundary value problem arising from the wave diffraction problem with a reactance condition. We consider the problem in a weak formulation within Bessel potential spaces, and where both cases of a complex and a pure real wave number are analyzed. Using the potential method, the boundary value problem is converted into a system of integral equations. The invertibility of the corresponding matrix pseudodifferential operator is shown in appropriate function spaces which allows the conclusion about the existence and uniqueness of a weak solution to the original problem. Higher regularity properties of solutions are also proved to exist in some scale of Bessel potential spaces, upon the corresponding smoothness improvement of given data. In particular, the 𝐶 α -smoothness of solutions in a neighbourhood of the screen edge is established with arbitrary α < 1 in the two-dimensional case and α < 1/2 in the three-dimensional case.

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