B. J. King

Calculation of Spheroidal Wave Functions

FORTRAN computer programs have been developed which accurately and rapidly evaluate for a wide range of parameters both prolate and oblate spheroidal radial wave functions of the first and second kind and their first derivatives, and both prolate and oblate spheroidal angle wave functions of the first kind and their first and second derivatives. This letter briefly discusses available documentation on these programs and describes some of the computational procedures necessary for their success. In addition, recently published tables of spheroidal radial wave functions calculated using these programs are described.

Self and mutual acoustic radiation impedances for two coplanar unbaffled disks

The self and mutual acoustic radiation impedances for two coplanar unbafed disks are calculated by using an eigenfunction expansion in terms of oblate spheroidal wave functions. Terms representing outgoing waves from both disks are included. One disk is assumed to be vibrating with a rotationally symmetrical normal velocity distribution, and the other disk is assumed to be stationary. The determination of the expansion coefficients from these boundary conditions is facilitated by the use of an addition theorem which expresses spheroidal wave functions with reference to one coordinate frame in terms of spheroidal wave functions with reference to a second coordinate frame. Numerical results for the special cases where the vibrating disk is either oscillating uniformly or vibrating uniformly on only one side are presented and discussed.

Spheroidal Wave Functions: Their Use and Evaluation

The Helmholtz or scaler wave equation (▿2 + k2) ψ = 0 is separable in both oblate and prolate spheroidal coordinates. Solutions to this equation constitute an essential element in the numerical calculation of the diffraction, radiation, and scattering of acoustic and electromagnetic waves by spheroids. They also find considerable application in other areas such as signal processing and nuclear models. FORTRAN computer programs have been developed to evaluate both efficiently and accurately the radial and angular parts of the solution in both oblate and prolate spheroidal coordinates. Extensive tables of oblate and prolate radial functions containing entries for values of h up to 40.0 and for values of the prolate radial coordinate as low as 1.00000001 are being published. (h = kd/2, where d is the interfocal distance.) These tables as well as the capabilities of the capabilities of the various computer programs are discussed. Examples illustrating the use of this coordinate system in acoustic radiation ca...

Electroacoustic modeling of magnetostrictive shells and rings

The mathematical model of the electroacoustic performance of a force‐driven free‐flooding magnetostrictive cylinder shell used as an underwater sound transducer, originally presented at the 86th Meeting of the Acoustical Society of America in 1973 [J. Acoust. Soc. Am. 55, 471(A) (1974)] and later developed in NRL Report 7767 (Dec. 1974), has been coded into a computer program called EIGSHIP. This program is designed to predict electrical and mechanical impedances of the loaded shell, transmitting responses, electroacoustic efficiency, surface velocities, farfield beam patterns, and other relevant performance parameters. An experimental check on the predictive capabilities of EIGSHIP was undertaken using three specially constructed magnetostrictive shells which were tested under water load conditions in an indoor test facility. A discussion of the comparison of predicted and measured performance is presented. Also samples of typical computer runs are displayed and commented on.

Self and Mutual Acoustic Radiation Impedances for Two Coplanar Unbaffled Disks

The self and mutual acoustic radiation impedances for two coplanar unbaffled disks are calculated using an eigenfunction expansion in terms of oblate spheroidal wave functions. Terms representing outgoing waves from both disks are included. One disk is assumed to be vibrating with a rotationally symmetrical normal velocity distribution, and the other disk is assumed to be stationary. The determination of the expansion coefficients from these boundary conditions is facilitated by the use of an addition theorem which expresses spheroidal wave functions with reference to one coordinate frame in terms of spheroidal wave functions with reference to a second coordinate frame. Numerical results for the special cases where the vibrating disk is either oscillating uniformly or vibrating uniformly on only one side are presented and discussed.

Acoustic Radiation from Two Spheroids

The acoustic radiation from two spheroids whose surface normal velocity distributions are specified is calculated using a Greens function approach. To simplify the analysis only axially symmetrical problems are considered. The necessary Greens function is expanded in spheroidal wave functions about both spheroids. The unknown expansion coefficients are determined from the boundary condition that the normal derivative vanishes over both surfaces. An addition theorem which expresses spheroidal wave functions in one coordinate system in terms of spheroidal wave functions in another coordinate system was developed to facilitate application of this boundary condition. Numerical results for several different two‐spheroid configurations and velocity distributions are presented and discussed. The straightforward extension to nonaxisymmetrical problems and to more than two spheroids is also discussed.