A special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions

1986 ◽  
Vol 80 (4) ◽  
pp. 1241-1247 ◽  
Author(s):  
A. F. Seybert ◽  
B. Soenarko ◽  
F. J. Rizzo ◽  
D. J. Shippy
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Acoustic Radiation ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Special Integral ◽  
Axisymmetric Bodies

Improved Integral Formulation for Acoustic Radiation Using Integral Equation of Frequency Averaged Quadratic Pressure

2017 ◽  
Vol 25 (01) ◽  
pp. 1750004 ◽  
Author(s):  
Honglin Gao ◽  
Sheng Li
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Acoustic Radiation ◽  
Boundary Integral ◽  
Uniqueness Of Solutions ◽  
High Frequencies ◽  
Numerical Examples ◽  
Integral Equation Formulation

This paper is concerned with the problem of obtaining a unique solution for radiation at irregular frequencies when an integral equation of frequency averaged quadratic pressure (FAQP) is used to get robust predictions at medium and high frequencies. It is proved that there is no unique solution of the integral equation of FAQP at irregular frequencies, and existence and uniqueness of solutions under four types of boundary conditions are discussed. A combined energy boundary integral equation formulation (CEBIEF) is presented and proves to be efficient to overcome the nonuniqueness of the integral equation of FAQP. The numerical examples are given to demonstrate the versatility of the CEBIEF method with a proposed function correctly indicating a solution.

scholarly journals On the solutions of mixed plane problems that are unbounded where the boundary conditions change

2001 ◽  
Vol 32 (3) ◽  
pp. 173-180
Author(s):  
M. G. El-Sheikh ◽  
V. N. Gavdzinski ◽  
A. E. Radwan
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Infinite System ◽  
Original Method ◽  
Plane Boundary ◽  
Algebraic Equations ◽  
Typical Problem ◽  
Equation Formulation ◽  
Integral Equation Formulation

In this paper, we apply a modification to the method of the integral equation formulation of mixed plane boundary value problems so that it enables us to obtain the solutions unbounded at the points where the boundary conditions change. Such solutions are of great physical interest. The modification is illustrated by means of a typical problem. As is it the case in the original method proposed by Cherskii [1], the problem is reduced to an infinite system of algebraic equations. The justification of the truncation of such systems has been established.

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