scholarly journals An integral‐equation numerical solution for the acoustical vibrations in an axisymmetric cavity of arbitrary cross section

1976 ◽  
Vol 59 (S1) ◽  
pp. S32-S33
Author(s):  
D. J. Henkel ◽  
L. H. Sobel
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Axisymmetric Cavity

Application of Method of Moments to Acoustic Scattering From Fluid Filled Cylinders Using Three Different Formulations

1995 ◽  
Author(s):  
S. P. Sun ◽  
P. K. Raju ◽  
S. M. Rao
Keyword(s):  
Integral Equation ◽  
Cross Section ◽  
Method Of Moments ◽  
Acoustic Scattering ◽  
Arbitrary Cross Section ◽  
The Body ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Equivalent Problems ◽  
Field Integral

Abstract In this work, we present three different formulations Viz. The pressure field integral equation formulation (PFIE), the velocity field integral equation formulation (VFIE), and the combined field integral equation formulation (CEDE) for solving acoustic scattering problems associated with two dimensional fluid-filled bodies of arbitrary cross section. In particular using the boundary conditions on the surface of the body, two equivalent problems, each valid for the outside and inside regions of the scatterer, are derived. By properly selecting the associated equations for these equivalent problems, the three different formulations are derived. The PFIE, VFIE, and CFIE are then solved by approximating the cylindrical cross section by linear segments and employing the method of moments. Further, it is shown that the moment matrices generated by the PFIE and VFIE are ill-conditioned at resonant frequencies of the cylinder, whereas the CFIE generates a well-conditioned matrix at all frequencies. The solution techniques presented in this work are simple, efficient and applicable to truly arbitrary geometries. Numerical results are presented for certain canonical shapes and compared with other available data.

Two-dimensional oscillations in a canal of arbitrary cross-section

1965 ◽  
Vol 61 (3) ◽  
pp. 827-846 ◽  
Author(s):  
A. M. J. Davis
Keyword(s):  
Integral Equation ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Inviscid Fluid ◽  
Degenerate Kernel ◽  
Two Dimensional ◽  
Small Kernel ◽  
Uniform Cross Section ◽  
Set Up ◽  
Image Position

AbstractAn infinitely long canal with uniform cross-section is filled with inviscid fluid. It is required first to show that any small two-dimensional motion of the fluid can be represented as the superposition of normal mode disturbances. A suitable generalized Green's function G(x, y; ξ) is constructed and is used to set up an integral equation (2·9) for the velocity potential on the free surface. It is shown that the eigenfunctions are complete and so are their (possibly time-dependent) extensions to the whole canal, in the sense that an arbitrary disturbance possesses a unique representation. In section 5, it is required to find asymptotic approximations to the large eigenvalues of (2·9). For this purpose a different integral equation (5·5) is set up on the canal, the kernel of which is the sum of a degenerate kernel and a small kernel. The solutions of this equation can therefore be obtained by iteration. The form of the mth eigenvalue is shown to befor sufficiently large m.

Oscillating Flow in Ducts of Arbitrary Cross Section

1969 ◽  
Vol 73 (706) ◽  
pp. 894-896
Author(s):  
A. M. Abu-Sitta ◽  
D. G. Drake
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Numerical Solution ◽  
Cross Section ◽  
Circular Cross Section ◽  
Arbitrary Cross Section ◽  
Oscillating Flow ◽  
Elliptic Case ◽  
Uniform Cross Section

The rectilinear flow of an incompressible viscous fluid along a duct of uniform cross section due to an oscillating pressure gradient has been considered by a number of investigators. The duct of circular cross .section has been treated by Richardson and Tyler and Sexl, the elliptic case by Khamrui, and the rectangular case by Drake and Fan and Chao. Recently Jeng has discussed the importance of this type of flow and has given a procedure for calculating a numerical solution for a duct of arbitrary cross-section. An interesting feature of these flows is that, at large frequencies when the flow is of boundary-layer type, the velocity at any instant has its maximum near the walls, the velocity overshooting its almost uniform distribution at the centre of the duct.

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