ON ONE PROBLEM IN INFINITY STRIP FOR BIAXISYMMETRIC HELMHOLZ EQUATION

Boundary value problem with special conditions on line y = 0 in infinity strip 0lt;xlt;a for generalized biaxisymmetric Helmholz equation is set. Conditions of this problem set difference of some one-sided limits of known functions. Unknown function is zero in the right boundary and in infinity. Unknown functions with weight for one parameter ц value and without weight for other. Existence of solution is proved for some conditions. Uniqueness of solutions is proved for other some conditions.

WAVE FORCES ON A ROW OF CYLINDRICAL PILES OF LARGE DIAMETER

In order to determine wave forces on a row of three cylindrical piles (Figure 2), a numerical computation procedure was applied using a solution of the Helmholz equation, in which the scattered wave field is described as the result of a series of singular sources located along the circumference of the pile [^Berkhoff, 1976, reference lj . Results of the computations were verified by means of model experiments, using both regular and irregular waves. It is shown that for the two pile geometries, included in the study, strong mutual interference will occur, resulting in transverse forces which are much higher than those found for single piles.

Lower Bounds to the Nth Eigenvalue of the Helmholz Equation Over Three-Dimensional Regions of Arbitrary Shape

A method is presented to compute a lower bound to the nth eigenvalue of the Helmholtz equation over three-dimensional regions. The shape of the regions is arbitrary and only their volume need be known.

XXI—The Whittaker-Hill Equation and the Wave Equation in Paraboloidal Co-ordinates

SynopsisThe problem considered is that of obtaining solutions of the Helmholz equation ∇2V + k2V = 0, suitable for use in connection with paraboloidal co-ordinates. In these co-ordinates the Helmholz equation is separable, and each of the separated equations is reducible to Hill's equation with three terms (the Whittaker-Hill equation). The properties of solutions of this equation are developed sufficiently to make possible the formal solution of simple boundary-value problems for paraboloidal surfaces, principally for the case k2 < 0.