Scattering of SH-Waves to Semi-Cylindrical Canyon and Rectangular Elastic Hill on the Ground

2012 ◽  
Vol 610-613 ◽  
pp. 2544-2551
Author(s):  
Wen Pu Shi
Keyword(s):  
Half Space ◽  
Function Method ◽  
Expansion Method ◽  
Free Boundaries ◽  
Sh Waves ◽  
Green Function Method ◽  
Common Boundary ◽  
Wave Function Expansion Method ◽  
The Common ◽  
The Given

Wave function expansion method and Green function method were employed to study thescattering problem of SH-waves to the semi-cylindrical canyon and rectangular hill on the gr ound. First, the displacements in the half space and rectangular hill were given which can santisfy the stress-free conditions on the free boundaries. Then, the first kind of Fredholm integration equation of the unknown distribution stress was obtained by using the displacement conditions on the common boundary between the half-space and the rectangular hill, and Gauss-Legendre integration formula was used to solve the equation. The given example results show the feasibility and practicability of the method here.

Effects of Surface Energy on Scattering of SH Waves by an Elastic Half-Plane with a Semi-Cylindrical Cavity

2012 ◽  
Vol 627 ◽  
pp. 698-704
Author(s):  
Zhi Ying Ou ◽  
Xiao Wei Liu ◽  
Qiong Deng
Keyword(s):  
Surface Energy ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Shear Waves ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Stress Fields ◽  
Sh Waves ◽  
Wave Function Expansion Method ◽  
Incident Waves

When the radius of materials and structral devices reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the frame of surface elasticity, the scattering of anti-plan shear waves by an elastic half-plan with a semi-cylindrical cavity considered the surface energy are investigated in this paper. When the boundary condition at the straight edge of the half-plan is traction free, the analytical solutions of stress fields of the half plan with semi-culindrical cavity are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of anti-plan shear waves as the radius of the semi-cylindrical cavity shrinks to nanoscale. The effects of incident waves with different frequencies and incident angel, radius of semi-cylindrical cavity and surface energy on the dynamic stress concentration around the semi-cylindrical cavity are discussed in detail.

The diffraction of SH waves by an arbitrary shaped crack in two dimensions

1992 ◽  
Vol 340 (1659) ◽  
pp. 503-529 ◽  
Keyword(s):  
Function Method ◽  
Scattering Problem ◽  
Elastic Solid ◽  
Two Dimensions ◽  
General Shape ◽  
Sh Waves ◽  
Green Function Method ◽  
Rigid Barrier ◽  
Shaped Crack ◽  
Scalar Scattering

In this paper we consider the two-dimensional scalar scattering problem for Helmholtz’s equation exterior to a smooth open arc of general shape. The problem has a number of physical applications including the diffraction of sound by a rigid barrier immersed in a compressible fluid and by a crack in an elastic solid which supports a state of anti-plane strain (SH-motion). The mathematical method used here is the crack Green function method introduced by G. R. Wickham. This enables the scattering problem to be reduced to the solution of a Fredholm integral equation of the second kind with a continuous kernel. The numerical solution of this equation is discussed and a number of examples are computed.

The Interaction of a Cylindrical Elastic Inclusion with Semicircular Disconnected Curve and Linear Cracks in an Homogeneous Medium by SH-Waves

2007 ◽  
Vol 348-349 ◽  
pp. 357-360
Author(s):  
Qi Hui ◽  
Jia Xi Zhao
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Function Method ◽  
Dynamic Stress ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Dynamic Stress Intensity Factor ◽  
Homogeneous Medium ◽  
Sh Waves

The scattering of SH waves by a cylindrical elastic inclusion with a semicircular disconnected curve and linear cracks in an homogeneous medium is investigated and the solution of dynamic stress intensity factor is given by Green’s function, complex function method. Firstly, we can divide the space into up-and-down parts along the X axis. In the lower half space, a new suitable Green’s function for the present problem is constructed.In the upper half space, the Green’s function has been given by reference [5]. Thereby the semicircular disconnected curve can be constructed when the two parts are bonded along the interface and the linear cracks can be constructed using the method of crack-division and the integral equations can be obtained by the use of continuity conditions at the X axis. Finally, some examples and results of dynamic stress intensify factor are given and the influence of the parameters is discussed.

scholarly journals Surface Motion of a Half-Space Containing an Elliptical-Arc Canyon under Incident SH Waves

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1884
Author(s):  
Hui Qi ◽  
Fuqing Chu ◽  
Jing Guo ◽  
Runjie Yang
Keyword(s):  
Wave Function ◽  
Half Space ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Expansion Method ◽  
Numerical Results ◽  
Mathieu Function ◽  
Axis Ratio ◽  
Function Expansion ◽  
Wave Function Expansion Method

The existence of local terrain has a great influence on the scattering and diffraction of seismic waves. The wave function expansion method is a commonly used method for studying terrain effects, because it can reveal the physical process of wave scattering and verify the accuracy of numerical methods. An exact, analytical solution of two-dimensional scattering of plane SH (shear-horizontal) waves by an elliptical-arc canyon on the surface of the elastic half-space is proposed by using the wave function expansion method. The problem of transforming wave functions in multi-ellipse coordinate systems was solved by using the extra-domain Mathieu function addition theorem, and the steady-state solution of the SH wave scattering problem of elliptical-arc depression terrain was reduced to the solution of simple infinite algebra equations. The numerical results of the solution are obtained by truncating the infinite equation. The accuracy of the proposed solution is verified by comparing the results obtained when the elliptical arc-shaped depression is degraded into a semi-ellipsoidal depression or even a semi-circular depression with previous results. Complicated effects of the canyon depth-to-span ratio, elliptical axis ratio, and incident angle on ground motion are shown by the numerical results for typical cases.

THE EU SUGAR MARKET PROFILE AND ITS MAIN DRIVERS

2015 ◽  
Author(s):  
Lubos SMUTKA ◽  
Irena BENEŠOVÁ ◽  
Patrik ROVNÝ ◽  
Renata MATYSIK-PEJAS
Keyword(s):  
Market Failure ◽  
Current System ◽  
Quota System ◽  
Considerable Debate ◽  
Sugar Market ◽  
The Common ◽  
The One ◽  
Production Capacities ◽  
The Given ◽  
The Eu

Sugar is one of the most important elements in human nutrition. The Common Market Organisation for sugar has been a subject of considerable debate since its establishment in 1968. The European agricultural market has been criticized for its heavy regulations and subsidization. The sugar market is one of the most regulated ones; however, this will change radically in 2017 when the current system of production quotas will end. The current EU sugar market changed is structure during the last several decades. The significant number of companies left the market and EU internal sugar market became more concentrated. The aim of this paper is presentation characteristics of sugar market with respect to the supposed market failure – reduction in competition. The analysis also identifies the main drivers and determinants of the EU especially quota sugar market. In relation to paper’s aim the following results are important. The present conditions of the European sugar market have led to market failure when nearly 75 % (10 million tonnes) of the quota is controlled by five multinational companies only. These multinational alliances (especially German and French one) are also taking control over the production capacities of their subsidiaries. In most countries, this causes serious problems as the given quota is controlled by one or two producers only. This is a significant indicator of market imperfection. The quota system cannot overcome the problem of production quotas on the one hand and the demand on the other; furthermore, it also leads to economic inefficiency. The current EU sugar market is under the control of only Sudzucker, Nordzucker, Pfeifer and Langen, Tereos and ABF.

The Still Life of Objects – Heidegger, Schapiro, and Derrida reconsidered

2015 ◽  
Vol 60 (1) ◽  
pp. 81-102
Author(s):  
KErstin Thomas
Keyword(s):  
Still Life ◽  
Work Of Art ◽  
Concrete Material ◽  
Vincent Van Gogh ◽  
Starting Point ◽  
Specific Object ◽  
Truth Claims ◽  
The Common ◽  
Critical Intervention ◽  
The Given

Kerstin Thomas revaluates the famous dispute between Martin Heidegger, Meyer Schapiro, and Jacques Derrida, concerning a painting of shoes by Vincent Van Gogh. The starting point for this dispute was the description and analysis of things and artworks developed in his essay, “The Origin of the Work of Art”. In discussing Heidegger’s account, the art historian Meyer Schapiro’s main point of critique concerned Heidegger’s claim that the artwork reveals the truth of equipment in depicting shoes of a peasant woman and thereby showing her world. Schapiro sees a striking paradox in Heidegger’s claim for truth, based on a specific object in a specific artwork while at the same time following a rather metaphysical idea of the artwork. Kerstin Thomas proposes an interpretation, which exceeds the common confrontation of philosophy versus art history by focussing on the respective notion of facticity at stake in the theoretical accounts of both thinkers. Schapiro accuses Heidegger of a lack of concreteness, which he sees as the basis for every truth claim on objects. Thomas understands Schapiro’s objections as motivated by this demand for a facticity, which not only includes the work of art, but also investigator in his concrete historical perspective. Truth claims under such conditions of facticity are always relative to historical knowledge, and open to critical intervention and therefore necessarily contingent. Following Thomas, Schapiro’s critique shows that despite his intention of giving the work of art back its autonomy, Heidegger could be accused of achieving quite the opposite: through the abstraction of the concrete, the factual, and the given to the type, he actually sets the self and the realm of knowledge of the creator as absolute and not the object of his knowledge. Instead, she argues for a revaluation of Schapiro’s position with recognition of the arbitrariness of the artwork, by introducing the notion of factuality as formulated by Quentin Meillassoux. Understood as exchange between artist and object in its concrete material quality as well as with the beholder, the truth of painting could only be shown as radically contingent. Thomas argues that the critical intervention of Derrida who discusses both positions anew is exactly motivated by a recognition of the contingent character of object, artwork and interpretation. His deconstructive analysis can be understood as recognition of the dynamic character of things and hence this could be shown with Meillassoux to be exactly its character of facticity – or factuality.

scholarly journals On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices

2021 ◽  
Author(s):  
Teresa Estañ ◽  
Natividad Llorca ◽  
Ricardo Martínez ◽  
Joaquín Sánchez-Soriano
Keyword(s):  
Budget Allocation ◽  
Pareto Efficiency ◽  
Claims Problems ◽  
The Common ◽  
The Given

AbstractIn this paper we study the class of claims problems where the amount to be divided is perfectly divisible and claims are made on indivisible units of several items. Each item has a price, and the available amount falls short to be able to cover all the claims at the given prices. We propose several properties that may be of interest in this particular framework. These properties represent the common principles of fairness, efficiency, and non-manipulability by merging or splitting. Efficiency is our focal principle, which is formalized by means of two axioms: non-wastefulness and Pareto efficiency. We show that some combinations of the properties we consider are compatible, others are not.

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