A new representation for the time-dependent surface pressure on a fluid-loaded shell of revolution with a prescribed space and time-dependent axisymmetric velocity distribution is presented. This representation, which is based on expanding the surface traction and velocity vectors into in-vacuo modal vector expansions with time-dependent coefficients, results in each time-dependent modal pressure coefficient being expressed as a sum of temporal convolution integrals which involve time-dependent modal radiation impulse responses and modal velocities. After presenting the formulation of the appropriate initial-boundary value problem, Fourier transform methods are introduced to obtain the corresponding Neumann boundary value problem. The solution of this latter problem is formulated as a minimum mean square error problem in which linear monopole harmonic distributions along the axis of the shell are introduced to determine the surface pressures resulting from the normal components of the modal vectors of interest. Singular value decomposition methods are then used to determine the harmonic monopole distributions. Modal decomposition and inverse Fourier transform methods are then used to evaluate the time-dependent modal radiation impulse responses. Numerical results are presented for the self and mutual modal radiation impulse responses for both spherical and spheroidal shells.

A new method is presented to evaluate the acoustic transient radiation from fluid-loaded shells of revolution which are excited by axisymmetric mechanical or acoustical excitations. This method is based on the use of an in-vacuo modal vector (eigenvector) expansion with time-dependent coefficients to describe the velocity field of the fluid-loaded shell. Modal acoustic impulse responses which account for the coupling between the in-vacuo modal vectors for the fluid-loaded shell are introduced in the formulation of the general solution. The time-dependent modal velocity coefficients are expressed as the solution of a set of coupled convolution integral equations which are readily solved by marching forward in time. The associated time-dependent surface pressure is subsequently expressed as a modal vector expansion in which the time-dependent coefficients are readily related to the modal velocity coefficients. Since the surface velocity and pressure are then known, the time-dependent pressures in the field are simply obtained via quadrature methods from the space-time Kirchhoff integral solution. The special case of a fluid-loaded spherical shell is addressed to illustrate the application of the method to determine the general characteristics of the transient velocity response of the shell and the associated pressure field resulting from axisymmetric mechanical force excitations of spherical shells. Numerical results are presented to illustrate the effects on the velocity response and pressure field of time-dependent fluid coupling between the modal vectors corresponding to the upper and lower branches of the in-vacuo frequency spectrum of the spherical shell.

The time-dependent pressure radiated from a finite, rigid, circular duct of constant cross section is determined for the specified motion (velocity or acceleration) of a piston source within the duct. The modal composition of the internal field variables is represented as an eigenfunction expansion over the duct cross section, and a time- and space-dependent Green’s function is used to develop a generalized boundary condition which describes the effect of the external surroundings at the duct exit. Solution of this boundary value problem results in a duct transfer function which is then cascaded with the spatial transfer function connecting the duct exit port and a selected external field point. In this paper, inversion to the time domain is accomplished via the FFT algorithm. Numerical examples demonstrating the calculation of the external time-dependent pressure are presented based upon the specification of a gated sinewave piston acceleration over an assumed piston spatial profile. Confirming the theoretical analysis, the numerical results show that the time-dependent pressure for the cross modes develops its peak value off-axis and is always zero on-axis, while the plane wave mode always peaks precisely on-axis.

Impulse response time domain and angular spectrum or wave vector time-domain methods can be used to investigate the spatial temporal characteristics of acoustic fields from planar ultrasonic transducers which are subjected to pulsed wideband excitations. Both methods are developed here from the time-dependent Green’s function solution of the initial-boundary value problem. The close relationship of the methods is made apparent by the use of spatial-temporal Fourier transform techniques of analysis. Axisymmetric fields are then addressed as a special case via the use of Hankel and Fourier transform techniques. Finally, classical solutions to the associated harmonic boundary value problems are then shown to result from temporal Fourier transforms of the time-dependent field solutions.

A wave vector, time-domain (k−t) method of forward projecting time-dependent pressure fields from complex vibrators is developed using space-time Fourier transform methods. Axisymmetric fields are included as a special case of the general formulation in which a pressure field at one plane can be forward projected to other planes. In brief, a wave vector, time-domain representation of the field at one plane is forward projected via a temporal convolution with a wave vector, time-domain impulse response that is dependent on the projection distance. The projected field is then obtained via the use of an inverse spatial Fourier transform. A numerical study of the method illustrates the accuracy of the approach when implemented using fast Fourier transform (FFT) algorithms. The forward projections of simulated pressure fields from a planar ultrasonic transducer are shown to be in excellent agreement with corresponding results from the use of a time-domain impulse response method.

A new technique for evaluating the self and mutual radiation impedances corresponding to the normal modes of a fluid loaded rectangular vibrator mounted in an infinite baffle is presented. The technique is based on the use of a time dependent angular spectrum formulation which leads to double integral representation for self and mutual impulse responses. Since the time limited impulse responses correspond to the inverse Fourier transforms of the self and mutual radiation impedances, the impedances can be readily obtained via the use of standard FFT methods. The advantages of the present approach relative to classical approaches will be presented. Numerical results will then be presented to illustrate the characteristics of the self and mutual impulse responses and radiation impedances for various mode shapes of interest. [Work supported by ONR.]

A review of linear acoustic transient phenomena in active arrays is presented. Such transients occur as a result of the finite bandwidth of the elements, the time delay caused by the propagation effects in the medium, and acoustic interaction effects among the elements. The characteristics of acoustic radiation from a time dependent monopole and dipole sources are first discussed to address such phenomena. These results are then extended to distributed sources where the importance of edge effects is clearly observed and discussed. Retarded potential methods to account for the effects of boundaries on the transient acoustic field are then presented. Such methods led to the development of impulse response techniques of evaluating acoustic transient phenomena. The impulse response technique is discussed in detail and numerical results are presented to illustrate transient acoustic pressure field and element interaction phenomena in active arrays.

An approach is presented to backward project an acoustic harmonic wavefield to the vibrating cylindrical source of the field. The approach is based on expanding the known pressure field on a cylindrical surface of the fluid into a series of circumferential modes with axially varying coefficients. After Fourier transforming the coefficients, each mode can be back projected to the source via the use of a backward propagator in the transform domain. As a result of the use of FFT methods the modal characteristics of the backward projected acoustic nearfield and/or the radial surface velocity of a finite cylindrical vibrator with a general velocity can be readily investigated. Numerical results are presented to illustrate the types of numerical problems and the resolution which can be obtained via the use of the method.

A numerical approach is presented to evaluate the surface intensity and radiation loading on a finite cylindrical surface with a known harmonic radial velocity distribution. The approach is based on a combined FFT and Green's function method [P. Stepanishen and H. W. Chen, J. Acoust. Soc. Am. Suppl. 1 73, S22 (1983)]. Surface pressure, intensity, and radiation loading are rapidly obtained via the use of standard FFT methods. The spatial fluctuations of the surface pressure and intensity for a known velocity distribution can thus be readily investigated. Numerical results are presented to illustrate the spatial variation of surface pressure and intensity as a function of axial mode shape, circumferential mode number, and frequency. Negative intensity regions and edge effects are clearly observed in the results at low frequencies.

This paper presents an extension of earlier works in investigating the acoustic nearfield of planar harmonic vibrators via the use of FFT methods [P. Stepanishen and K. Benjamin, J. Acoust. Soc. Am. 71, 803–812 (1982)]. In the present paper, a numerical approach is presented to evaluate the acoustic nearfield of baffled cylindrical vibrators with specified harmonic radial velocity distributions. The approach is based on the use of a combined Green's function and FFT method. The acoustic field is first represented in terms of a Fourier transform of the specified radial velocity and the resulting spectral representation is then rapidly evaluated via the use of FFT methods to obtain the spatial characteristics of the acoustic field. Extensive numerical results are presented to illustrate the spatial characteristics of the acoustic fields of finite length vibrators with axisymmetric and nonaxisymmetric distributions.

Acoustic scattering and transmission of wide-band plane waves by fluid loaded plates is addressed using Timoshenko–Mindlin plate theory. The solution for the case of an impulsive excitation is first developed via the use of a double Fourier transform method. This solution is then used to develop the solutions for the scattered and transmitted fields corresponding to an arbitrary pulsed excitation via convolution integral relationships. The characteristics of the impulsive solutions are investigated as a function of incident angle. Precursors, which are due to the dispersive nature of flexural waves in the plate, are noted to occur in certain angular ranges. The nature of the precursors, and hence the impulse responses, are discussed.