scholarly journals INPUT ADMITTANCES ARISING FROM EXPLICIT SOLUTIONS TO INTEGRAL EQUATIONS FOR INFINITE-LENGTH DIPOLE ANTENNAS

2005 ◽  
Vol 55 ◽  
pp. 285-306 ◽  
Author(s):  
George Fikioris ◽  
Constantinos A. Valagiannopoulos
Keyword(s):  
Integral Equations ◽  
Explicit Solutions ◽  
Infinite Length ◽  
Dipole Antennas

Explicit Solutions of Integral Equations and Relations for Potentials

2018 ◽  
Vol 54 (9) ◽  
pp. 1202-1214
Author(s):  
P. A. Krutitskii ◽  
V. V. Kolybasova
Keyword(s):  
Integral Equations ◽  
Explicit Solutions

scholarly journals Ground Vibration Generated by a Harmonic Load Moving in a Circular Tunnel in a Layered Ground

2003 ◽  
Vol 22 (2) ◽  
pp. 83-96 ◽  
Author(s):  
X Sheng ◽  
C J C Jones ◽  
D J Thompson
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Ground Vibration ◽  
Boundary Integral ◽  
Infinite Length ◽  
Harmonic Load ◽  
Algebraic Equations ◽  
Force Method ◽  
Layered Ground ◽  
Element Method

All modes of transport impact on e environment. Although railways are seen as environmentally advantageous in many ways, the issues of noise and vibration are often seen as their weakness. For trains running in tunnels where direct airborne noise is effectively screened, structure-borne or ‘ground-borne’ noise caused by vibration propagated through the ground is the most important concern. The vibration of interest in this case has frequency components from about 15 Hz to 200 Hz. To understand the mechanisms of vibration propagation from tunnels, a predictive model has been developed for ground vibration generated by a stationary or moving harmonic load applied in a circular lined or unlined tunnel in a layered ground. This study is the first step towards the use of discrete wavenumber methods to model ground vibration from underground trains. Discrete wavenumber methods fall into three categories: the discrete wavenumber fictitious force method, the discrete wavenumber finite element method and the discrete wavenumber boundary element method. This study uses the discrete wavenumber fictitious force method. Based on the moving Green's functions for a layered half-space and those for a cylinder of infinite length, boundary integral equations over the tunnel-soil interface are established. Unlike the conventional boundary integral equation in elastodynamics, the method used here only requires the displacement Green's function. This is achieved by introducing the excavated part of the ground as an extra substructure. The boundary integral equations are further transformed into a set of algebraic equations by expressing each quantity involved in the boundary integral equations in terms of a Fourier series. Results presented in this paper illustrate the effect of a tunnel on vibration propagation at the ground surface and the difference between a lined tunnel and an unlined tunnel.

Explicit solutions for a class of dual integral equations

1982 ◽  
Vol 91 (3-4) ◽  
pp. 277-285 ◽  
Author(s):  
R. S. Anderssen ◽  
F. R. de Hoog ◽  
L. R. F. Rose
Keyword(s):  
Integral Equations ◽  
Explicit Solution ◽  
Explicit Solutions ◽  
Dual Integral Equations ◽  
Linear Combinations ◽  
Basic Technique ◽  
Image Position

SynopsisAn explicit solution is derived for the dual integral equationswhen A(ξ) takes the formIt is then shown how the basic technique can be adapted to derive explicit solutions for more general forms of A(ξ) such asandand linear combinations of such sums.

Two more hypergeometric integral equations

1967 ◽  
Vol 63 (4) ◽  
pp. 1055-1076 ◽  
Author(s):  
E. R. Love
Keyword(s):  
Integral Equations ◽  
Mathematical Society ◽  
Fractional Integrals ◽  
Explicit Solutions ◽  
Similar Form ◽  
Uniqueness Of Solutions ◽  
Hypergeometric Integral ◽  
Necessary And Sufficient

SummaryThis paper is a sequel to one with a similar title to appear in the Proceedings of the Edinburgh Mathematical Society. Explicit solutions are found for two more integral equations of similar form; and also conditions necessary and sufficient for existence, and sufficient for uniqueness, of solutions. These theorems are preceded by several preparatory theorems on fractional integrals with origin ∞, including integrals of purely imaginary order.

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