Francis Hugh Fenlon

Axisymmetric parametric radiation—A weak interaction model

In this paper the difference‐frequency field of a a parametric acoustic radiator is approximated via a weak finite‐amplitude solution of the second‐order nonlinear paraxial wave equation (i.e., the nonlinear optical analog established by E. A. Zabolotskaya and R. V. Khokhlov [Sov. Phys.–Acoust. 15, 35–40 (1969)]) obtained by expressing the primary waves of an axisymmetrically excited bifrequency piston projector in terms of a weighted sum of Gauss–Laguerre eigenmodes. By relating the fundamental (i.e., Gaussian) mode in the farfield of the projector to those of equivalent ’’Bessel beams’’ a closed‐form expression for the difference‐frequency field is thus obtained as a function of range. Following a review of the solution’s phenomenological properties comparisons are made of predicted results and experimental data reported in the literature.

On the Utilization of Ferrofluids for Transducer Applications

An assessment of the suitability of ferrofluids for acoustic transducer and receiver applications has led to the following conclusions: First, the magnetostrictive mode of operation is not efficient enough to offer an alternative to conventional solid materials in use. Second, the piston motion of the ferrofluid induced by an applied field gradient does provide a real alternative to conventional magnetostrictive transducers. For an applied static field of 4000 Oe and a field gradient of 1000 Oe/cm, it is possible to achieve an overall efficiency that is greater than that for the ferromagnetic solids. Third, ferrofluids appear to provide a desirable alternative for pressure‐sensing applications in severe environments (e.g., detonations) where piezoelectric and pyroelectric materials suffer fatigue and failure. Fourth, ferrofluids offer the prospect of obtaining broadband frequency response when radiating or receiving in liquid media.

Parametric acoustic array formation in dispersive fluids

The effect of dispersion on parametric arrays formed by Gaussian beams is investigated via solutions of the nonlinear paraxial wave equation. Analytical solutions are obtained by employing the quasilinear approximation; the results are thus restricted to weak nonlinear interactions. Axial field curves, farfield directivity patterns, and three‐dimensional field plots are presented for the difference‐frequency signal. The combined effects of dispersion, dissipation, and diffraction are considered in detail. Discrepancies with previous work are discussed. Solutions for the sum‐frequency and second‐harmonic components are also presented. A transformation is given to make the various solutions apply to arrays formed by primaries from a circular piston.

On the derivation of Zone I spectra for a pulsed finite‐amplitude source operating in a nonviscous nondispersive fluid medium

A mathematical procedure for deriving the complex spectral amplitudes generated by nonlinear interaction of the frequency components of a pulsed finite‐amplitude source in a nonviscous nondispersive fluid medium, within a distance prior to shock formation, is established. In order to illustrate the procedure, the nonlinear propagation spectra of a dual frequency pulse and a dual sweep linear FM pulse are derived.

Control of the directional response of acoustic transducer array elements on curved surfaces by modification of the diffracted field

The response of acoustic transducer elements mounted on a curved end cap on a cylinder, both of arbitrary surface impedance, for signals arriving from the rear, has been studied using the Geometrical Theory of Diffraction. A mathematical model has been generated, and results will be given for an element on an ellipsoidal end cap at several nondimensional frequencies and for several typical surface impedances, including some cases where the impedance is nonuniform.

On the derivation of a Lagrange‐Banta operator for progressive finite‐amplitude wave propagation in a dissipative fluid medium

In this paper, a classical operational solution of the nonlinear wave equation which defines the interaction (to second order) of progressive finite‐amplitude (intense) acoustic waves in lossless nondispersive fluids prior to shock formation is approximately extended to include the influence of viscous dissipation on the spatial rate‐of‐change of the nonlinearly generated spectral components.