Hankel Function Of First Kind Research Articles

Exact solution to Lippmann-Schwinger equation for a circular billiard

We present an exact solution to the Lippmann-Schwinger equation for a two-dimensional circular billiard. After diagonalizing an integral operator whose kernel is a zeroth order Hankel function of first kind, we use its eigenfunctions and eigenvalues to obtain in a straightforward way the exact wavefunctions of the referred Lippmann-Schwinger equation.

Circular elastic inclusions in cylindrical shells

The problem of a circular elastic inclusion in a cylindrical shell subjected to internal pressure or thermal loading is studied. The two shallow-shell equations governing the behaviour of a cylindrical shell are transformed into a single differential equation involving a curvature parameter and a complex potential function in a non-dimensional form. In the shell region, the solution is represented by Hankel functions of first kind, whereas in the inclusion region it is represented by Bessel functions of first kind. Boundary conditions at the shell-inclusion junction are expressed in a simple form involving in-plane strains and change in curvature. The effect of such inclusion parameters as extensional rigidity, bending rigidity, and thermal expansion coefficients on the stress concentrations has been determined. The results are presented in non-dimensional form for ready use

Anti-Plane Surface Disturbance

Solution to a problem of half-space subjected to anti-plane surface disturbance via Cagniard-de Hoop method has been investigated. The solution is very much dependent on the choice of branch cuts, branches, and their behavior along the appropriate selected contour. Investigations show that the contour, which simplifies the inversion integral, may or may not exist in some quadrants of x-plane and is very much dependent on the position of the point x. Consequently, the solution is the Hankel function of first kind . Key Words: Cagniard-de Hoop method. Inversion Integral. Hankel function. Anti-plane Shear. Waves propagation. Fourier Transform.