Diffraction of Pulses by Cylindrical Obstacles of Arbitrary Cross Section

1962 ◽  
Vol 29 (1) ◽  
pp. 40-46 ◽  
Author(s):  
M. B. Friedman ◽  
R. Shaw
Keyword(s):  
Shock Wave ◽  
Integral Equation ◽  
Cross Section ◽  
Analytical Solutions ◽  
Arbitrary Cross Section ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Dimensional Problem ◽  
Acoustic Shock Wave ◽  
Square Box

The two-dimensional problem of the diffraction of a plane acoustic shock wave by a cylindrical obstacle of arbitrary cross section is considered. An integral equation for the surface values of the pressure is formulated. A major portion of the solution is shown to be contributed by terms in the integral equation which can be evaluated explicitly for a given cross section. The remaining contribution is approximated by a set of successive, nonsimultaneous algebraic equations which are easily solved for a given geometry. The case of a square box with rigid boundaries is solved in this manner for a period of one transit time. The accuracy achieved by the method is indicated by comparison with known analytical solutions for certain special geometries.

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.

Application of coordinate transformation to two-dimensional scattering and diffraction problems

1969 ◽  
Vol 47 (7) ◽  
pp. 795-804 ◽  
Author(s):  
L. Shafai
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Cross Section ◽  
Coordinate Transformation ◽  
Scattered Field ◽  
Arbitrary Cross Section ◽  
Surface Currents ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
First Order

The two-dimensional problem of determining the electromagnetic field scattered by a cylinder of arbitrary cross section is reduced to the solution of first-order, coupled differential equations. The procedure for finding the surface currents, scattered field, and the scattering cross section for a perfectly-conducting cylinder is given in detail. A brief study of the scattering by a polygonal cylinder and n identical strips equally spaced azimuthally around the z axis is used to examine the behavior of the differential equations.

Derivatives and Parameter Designs of Arbitrary Cross-Section Inhomogenous Beams’ Modes

2013 ◽  
Author(s):  
J. W. Xing ◽  
G. T. Zheng
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Analytical Solutions ◽  
Structural Parameters ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Design Parameters ◽  
Structural Parameter ◽  
Highly Sensitive ◽  
Sensitivity Analysis Method

As highly sensitive to structural parameter variations, it is necessary to study relations between derivatives of displacement modes and structural design parameters. This paper proposes an integral technique for obtaining the analytical solutions of slope and curvature modes of arbitrary cross-section inhomogeneous cantilever beam. The method is validated by comparing the computation results of modal frequencies and shapes with both numerical and analytical solutions. Furthermore, based on the presented method, we have established explicit expressions for the structural parameters sensitivity of the slope/curvature mode shapes. An example of parameter design is also presented for a cantilever beam with the proposed sensitivity analysis method.

Long waves in a uniform channel of arbitrary cross-section

1968 ◽  
Vol 32 (2) ◽  
pp. 353-365 ◽  
Author(s):  
D. H. Peregrine
Keyword(s):  
Solitary Wave ◽  
Cross Section ◽  
Gravity Waves ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Arbitrary Cross Section ◽  
Long Waves ◽  
Order Of Approximation ◽  
Two Dimensional ◽  
Uniform Channel

Equations of motion are derived for long gravity waves in a straight uniform channel. The cross-section of the channel may be of any shape provided that it does not have gently sloping banks and it is not very wide compared with its depth. The equations may be reduced to those for two-dimensional motion such as occurs in a rectangular channel. The order of approximation in these equations is sufficient to give the solitary wave as a solution.

Two-dimensional toroidal MHD equilibria of arbitrary cross-section

1983 ◽  
Vol 29 (1) ◽  
pp. 173-175 ◽  
Author(s):  
Ferdinand F. Cap
Keyword(s):  
Equilibrium Problem ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Two Dimensional ◽  
New Approach ◽  
Mhd Equilibrium ◽  
Mhd Equilibria

A new approach to the solution of the MHD equilibrium problem is outlined.

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